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Solving Quadratic Equations

SET-UP:Remove all fractions and
parentheses, group like terms, make squared term positive,
and put in Standard Form:

Ax^{2} + Bx + C = 0

ALWAYS:Factor out any common factors first

2 TERMS

Missing 1^{st} Term
3x - 12 = 0

Not Quadratic!
(linear)

Solve for 1 answer
x = 12
x = 4

Missing 2^{nd} Term

Use Square Root Method

Missing 3^{rd}Term
x^{2} + 3 = 0

you forgot to factor
out the common “x”

isolate x^{2}
x = 12
both
sides

isolate squared binomial

both
sides

ALL 3 TERMS

By Factoring

By Completing the Square
2x^{2} - 6x - 3 = 0
coefficient of x^{2} must be 1:
divide both sides by 2:
complete the square:
add (½B)2 to both sides:
write as a binomial squared:
use Square Root Method:

B^{2}-4ac is called the discriminant
1) if B^{2}-4ac is positive: 2 real roots
2) if B^{2}-4ac is negative: 2 complex roots
3) if B^{2}-4ac = 0: 1 real root (twice)

Quadratic Formula

Remember: You must check both
solutions when you make a non-quadratic equation quadratic!