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2
The lefthand side is now a perfect square, and the righthand
side consists of a constant. We can now use the square root property to solve for x .
Example
1 Solve by completing the square: x 2 + 8x = −12. 2 Solve by completing the square: 2p 2 − 5p = 1. Outline Quadratic Equations Solving Quadratic Equations The General Solution of a Quadratic Equation
Suppose we complete the square and solve for x in the
quadratic equation ax 2 + bx + c = 0 (a = 0).
c
b
ax 2 + bx + c = 0 ⇒ x 2 + x = −
a
a
b
b2
b2
c
⇒ x2 + x + 2 = − + 2
a
4a
a 4a
b 2 b 2 − 4ac
=
⇒
x+
2a
4a 2
b
b 2 − 4ac
=±
2
2a
√ 4a
b
b 2 − 4ac
⇒ x =− ±
2a √
2a
−b ± b 2 − 4ac
⇒ x=
2a
⇒ x+ Applications Outline Quadratic Equations Solving Quadratic Equations The Quadratic Formula Theorem (The Quadratic Formula)
If ax 2 + bx + c = 0 (a = 0)...
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This note was uploaded on 02/10/2014 for the course MATH 1050 taught by Professor K.jplatt during the Spring '14 term at Snow College.
 Spring '14
 K.JPlatt
 Algebra, Equations

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