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

find all real or complex zeros by completing the squares

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# 1 Answer

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