completing the square x^2 + 4x=21

Question

i need help how to solve this equation.

Answer 1

The equation is x² + 4x = 21.

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

 Here x coefficient = 4. so, (half the x coefficient)² = (4/2)²= 4.

Add 4 to each side.

x² + 4x + 4 = 21 + 4

(x + 2)² = 25

(x + 2)² = (± 5)²

x + 2 = ± 5

x = - 2 + 5 and x = - 2 - 5

x = 3 and x = - 7

The roots are x = 3 and x = - 7.