g(x)=-8x^2+2x+7

Question

find all real or complex zeros by completing the squares

Answer 1

To find the zeros of a function, set the function equal to zero.

-8x² + 2x + 7 = 0                            Set the equation equal to zero

-8x² + 2x = -7                                Subtract 7 from each side

x² - (1/4)x = 7/8                            Divde each side by -8

            1/64                                  Find the "(b/2a)²" term by dividing 1/4 by 2 and squaring it

x² - (1/4)x + 1/64 = 7/8 + 1/64      Add 1/64 to each side

(x - 1/8)² = 7/8 + 1/64                  factor the left side into its perfect square componants

(x - 1/8)² = 56/64 + 1/64              Find the common denominator on the right side

(x - 1/8)² = 57/64                        Simplify the right side

x - 1/8 = +/- √(57/64)                  Take the square root of both sides

x - 1/8 = +/- √57/8                      Simplify the denominator (√64 = 8)

x = (1 +/- √57)/8                         Add 1/8 to each side