Section 1.5 Quadratic Equations

2 b1 add c2 to both sides 2 the left hand side is now

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Unformatted text preview: sides. 2 The left-hand side is now a perfect square, and the right-hand 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.

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