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How do you calculate an equation?

Solving equations involves finding the unknowns in the equation. Let's start with simple equations. You have an equation with one unknown - call it x. The trick here to solving the equation is to end up with x on one side of the equation and a number on the other. You do this by adding, subtracting, multiplying or dividing both sides of the equation. Remember, whatever you do to one side of the equation, you must do the same to the other side.

A quadratic equation is a second-degree polynomial having the general form ax²+bx+c=0, where a, b, and c are constants. There are multiple methods to solve quadratics: factorization, completing the square, and the quadratic formula.

First up is factorization. How do you factorize a quadratic? The trick is to get the equation to the form (x-u)(x-v)=0, now we have to solve much simpler equations.

Solving quadratics by factorizing usually works just fine. But what if the quadratic equation can't be factored, you're going to need a different method to help you solve it, completing the square.

An equation in which one side is a perfect square trinomial can be easily solved by taking the square root of each side. Easy is good, so we basically want to force the quadratic equation into the form (x+a)²=x²+2ax+a².

All it takes is making sure that the coefficient of the highest power (x²) is one. Move the constant term to the right hand side. Take half of the coefficient of the middle term(x), square it, and add that value to both sides of the equation. Factor the perfect square trinomial. Take the square root of each side and solve.

To make things simple, a general formula can be derived such that for a quadratic equation of the form ax²+bx+c=0 the solutions are x=(-b ± sqrt(b^2-4ac))/2a. The quadratic formula comes in handy, all you need to do is to plug in the coefficients and the constants (a,b and c).

Solving exponential equations is straightforward; there are basically two techniques:

If the exponents on both sides of the equation have the same base, you can use the fact that: If a^x=a^y then x=y. Now simply solve the equation.

In all other cases, take the log of both sides (this might require some manipulation) and solve for the variable. The logarithm property ln(a^x)=xln(a) makes this a fairly simple task.

Radical equations are equations involving radicals of any order. To solve radical equations, you first have to get rid of the radicals, in the case of square roots square both sides of the equation (in some cases this should be done multiple times), then simplify the new equation (either linear or quadratic) and solve. One more thing to note, by squaring the equation we changed the original equation, so it is very important to check the solutions at the end.

The key to solving equations is to identify the equation type. Other equation types to know are the biquadratic, rational, logarithmic, and absolute.

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How do you calculate an equation? Solving equations involves finding the unknowns in the equation. Let's start with simple equations. You have an equation with one unknown - call it x. The trick here to solving the equation is to end up with x on one side of the equation and a number on the other.

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Algebra is great fun - you get to solve puzzles!

With computer games you play by running, jumping and finding secret things.

With Algebra you play with letters, numbers and symbols, and you also get to find secret things!

And when you learn some of the "tricks" it becomes a fun challenge to work out how to use your skills in solving each question.

The Basics

Exponents

Simplifying

Factoring

Logarithms

Polynomials

Linear Equations

Quadratic Equations

Solving Word Questions

Functions

Sequences and Series

Where to Next?

Other Interesting Topics You May Like

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Algebra is great fun - you get to solve puzzles! With computer games you play by running, jumping and finding secret things. With Algebra you play with letters, numbers and symbols, and you also get to find secret things!

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What is an Equation

An equation says that two things are equal. It will have an equals sign "=" like this:

That equation says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement " this equals that"

Parts of an Equation

So people can talk about equations, there are names for different parts (better than saying "that thingy there"!)

Here we have an equation that says 4x − 7 equals 5, and all its parts:

A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y.

A number on its own is called a Constant.

A Coefficient is a number used to multiply a variable ( 4x means 4 times x, so 4 is a coefficient)

Variables on their own (without a number next to them) actually have a coefficient of 1 ( x is really 1x)

Sometimes a coefficient is a letter like a or b instead of a number:

Example: ax² + bx + c

An Operator is a symbol (such as +, ×, etc) that shows an operation (ie we want to do something with the values).

A Term is either a single number or a variable, or numbers and variables multiplied together.

An Expression is a group of terms (the terms are separated by + or − signs)

So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"

Exponents

The exponent (such as the 2 in x ²) says how many times to use the value in a multiplication.

Examples:

Exponents make it easier to write and use many multiplications

Polynomial

Example of a Polynomial: 3x² + x - 2

A polynomial can have constants, variables and the exponents 0,1,2,3,...

But it never has division by a variable.

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

Like Terms

Like Terms are terms whose variables (and their exponents such as the 2 in x ²) are the same.

In other words, terms that are "like" each other. (Note: the coefficients can be different)

Example:

Are all like terms because the variables are all

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An equation says that two things are equal. It will have an equals sign "=" like this: That equation says: what is on the left (x + 2) is equal to what is on the right (6) So an equation is like a statement " this equals that" So people can talk about equations, there are names for different parts (better than saying "that thingy there"!)

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Math patterns example 2 | Applying mathematical reasoning | Pre-Algebra | Khan Academy

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Math patterns example 1 | Applying mathematical reasoning | Pre-Algebra | Khan Academy

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Choose your own adventure from over 15 Visual Patterns! *Inspired by patterns at http://www.visualpatterns.org/ Feel free to have students use the following handout to: 1) Describe the pattern in their own words.

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How you can be good at math, and other surprising facts about learning | Jo Boaler | TEDxStanford

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1. Start with a triangle. 2. Shrink the triangle to half height, and put a copy in each of the three corners 3. Repeat step 2 for the smaller triangles, again and again, for ever!

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For example, if you toss a coin three times, there is only one combination that will give you three heads (HHH), but there are three that will give two heads and one tail (HHT, HTH, THH), also three that give one head and two tails (HTT, THT, TTH) and one for all Tails (TTT).