Solving Quadratic Equations

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SOLVING QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA

SOLVING LINEAR EQUATIONS

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Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

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Ineq. #3:

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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 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^rdTerm
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 (½B)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!