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Question

Solve the Equation x^2 + 10x = k by completing the square.

Answer 1

Completing square method

The equation x² + 10x  = k

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

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

Add 25 to each side

x² + 10x + 25 = k + 25

(x + 5)²= k + 25

Take square root both sides.

x + 5 = ± √(k + 25)

Solution x = - 5 + √(k + 25) and x = - 5 - √(k + 25).