Question

Solve the following quadratic equations by completing the square method.

1. 9y² – 12y + 2 = 0 

2. 2y² + 9y + 10 = 0 

3. 5x² = 4x + 7

Answer 1

1. 9y² – 12y + 2 = 0

2. 2y² + 9y + 10 = 0

Taking square root of both sides, we get

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

3. 5x² = 4x + 7 

∴ 5x² – 4x – 7 = 0

∴   x² - \(\frac{4}{5}\)x - \(\frac{7}{5}\) = 0  ...[Dividing both sides by 5]

if x² - \(\frac{4}{5}\)x + k = (x + a )², then

x² - \(\frac{4}{5}\)x + k = x² + 2ax + a²

Comparing the coefficients, we get

-\(\frac{4}{5}\) = 2a and k = a²