Question

Solve the following quadratic equations by completing the square method.

m² – 5m = -3

Answer 1

m² – 5m = -3 

∴ m² – 5m + 3 = 0 

If m² – 5m + k = (m + a)², then 

m² – 5m + k = m² + 2am + a²

Comparing the coefficients, we get

-5 = 2a and k = a²

Taking square root of both sides, we get

∴ The roots of the given quadratic equation are \(\frac{\sqrt{13} + 5}{2}\) and \(\frac{-\sqrt{13} + 5}{2}.\)