Question

After completing the square, what are the solutions to the quadratic equation below?

x^2 + 2x = 25

Answer 1

Completing the square Method :

The equation is x² + 2x = 25.

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

 Here x coefficient = 2. So, (half the x coefficient)² = (2/2)²= 1.

Add 1 to each side.

x² + 2x + 1 = 25 + 1

x² + 2(x)(1) + 1² = 26

Apply Perfect Square Trinomial : u² + 2uv + v² = (u + v)².

(x + 1)² = 26

x + 1 = ± √26

x = - 1 ± √26.

The option C is correct.