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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:

Ax2 + Bx + C = 0

ALWAYS: Factor out any common factors first

2 TERMS
Missing 1st Term
3x - 12 = 0

Not Quadratic!
(linear)

Solve for 1 answer
x = 12
x = 4

Missing 2nd Term

Use Square Root Method
Missing 3rdTerm
x2 + 3 = 0

you forgot to factor
out the common “x”

isolate x2
x = 12
both sides
isolate squared binomial

both sides
ALL 3 TERMS
By Factoring


By Completing the Square
2x2 - 6x - 3 = 0
coefficient of x2 must be 1:
divide both sides by 2:
complete the square:
add (┬ŻB)2 to both sides:
write as a binomial squared:
use Square Root Method:

 

B2-4ac is called the discriminant
1) if B2-4ac is positive: 2 real roots
2) if B2-4ac is negative: 2 complex roots
3) if B2-4ac = 0: 1 real root (twice)

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