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A Quadratic Equation is a second-degree polynomial that has at least one term with degree two and no term greater than degree two. All second-degree polynomials are quadratic.

The standard form for single variable quadratic equations is:

ax2 + bx + c = 0

Where x is the variable (or unknown), “a” is the coefficient of the variable squared, “b” is the coefficient of the variable to the first power, and “c” is the term that does not contain the variable. The coefficient “a” cannot equal 0.

There are two methods of solving these equations:

1. Factoring

Factoring begins with easier, special situation Pure Quadratics, and progresses to more difficult polynomial math requiring a Completing the Square method. Parabolic flight path of space ship near planet can be quadratic.

A quadratic polynomial without a first degree term having only a second degree term and constants is a Pure Quadratic. These are unique form equations and are easily solved by determining the square root of the constant.

To factor the pure quadratic x2 - 9:

(x + 3) (x - 3), then by FOIL,

x2 - 9 = 0 when x = ± 3

(square root of the constant 9 is ± 3)

FOIL (First - Outer - Inner - Last):

(x + 3) (x - 3) =

First:

x • x = x2

Outer:

x • -3 = -3x

Inner:

3 • x = 3x

Last:

3 • -3 = -9

x2 - 3x + 3x - 9 = x2 - 9

To factor the pure quadratic 3x2 - 15 = 0:

3x2 = 15

x2 = 15/3

x2 = 5

The roots of x2 are √5 and -√5

√x2 = ± √5, and x = ± √5