complete the square of f(x) = 4x^2 − 40x + 107

Question

Complete the square.

Answer 1

Let us assume f(x) = 4x² - 40x + 107 = 0.

4x² - 40x + 107 = 0

Divide each side by 4.

x² - 10x + 107/4 = 0

Separate variables and constants aside by subtracting 107/4 from each side.

x² - 10x = - 107/4

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = -10. so, (half the x coefficient)² = (-10/2)²= 25.

Add 25 to each side.

x² - 10x + 25 = - 107/4 + 25

(x - 5)² = -107+100/4 = - 7/4

(x - 5)² = ( ± sqrt(7) i/2)²

Take square root both sides.

x - 5 = ± sqrt(7)i/2

x = 5 ± sqrt(7)i/2.