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A quadratic equation in x is an equation that can be written in the general form ax ² + bx + c = 0, where a, b, and c are real numbers with a ≠ 0.
In this section, there are four methods for solving quadratic equations: factoring, exracting square roots, completing the square and the Quadratic Formula.

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Solve (3x + 4) x = 7
Original equation
(3x + 4)x = 7
Write in general form
3x2 + 4x – 7  = 0
Factor
(3x +7)(x – 1) = 0
Set 1st factor equal to 0
3x + 7 = 0 --> x = -7/3
Set 2nd factor equal to 0
x – 1 = 0  --> x = 1

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Solve x² = 9
Write original equation
x² = 9
Extract square roots
√x² = √9
Simplify radicals
x = ±3

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Solve x² + 10x + 9 = 0
Write in the form x ² + bx = c
x² + 10x = -9
Find (b/2 )2
(10/2)² = 5² = 25
Complete the square
x² +10x + 25 = -9 + 25
Factor and Simplify
(x + 5)² = 16
Take the square root of both sides
x + 5 = ±4
Write and solve two equations
x + 5 = 4 ; x + 5 = -4
x = -1 ; x = -9

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Solve 4x² + 3x – 2 = 0
a = 4 , b = 3 , c = -2
Plug these values into the formula and simplify to get the answer
x = -(3) √ (3)² - 4(4)(-2) / 2(4)
x = -3 ±√ 9 + 32 / 8
x = -3 ±√ 41 / 8

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Just remember: Quadratics always have an x ² term, possibly an x-term, and possibly a constant term! If your equation has an x2 term or will have an x2 term after multiplying out, it may be a quadratic, provided the other terms fit the form.