Question

5x2
-2 -6x =0. Find the roots by completeing the square.​

Answer 1

Given equation:

5x² - 2 - 6x = 0

• Make the coefficient of x² as 1.

(5x² - 6x - 2)/5 = x² - (6/5)x - (2/5) = 0

• Multiply the coefficient of x by 1/2. Add and subtract the square of the obtained number from the equation.

Coefficient of x = 6/5.

Multiply it by 1/2: 6/5 × 1/2 = 3/5

Add and subtract the square of this number: x² - (6/5)x + (3/5)² - (3/5)² - (2/5) = 0

• Solve the first three terms as the identity: a² - 2ab + b² = (a + b)²

x² - (6/5)x + (3/5)² - (3/5)² - (2/5) = 0

=> (x - 3/5)² - (9/25) - (2/5) = 0

• Take the other two left terms to LHS and solve.

=> (x - 3/5)² = (9/25) + (2/5)

=> (x - 3/5)² = (9 + 10)/25 [Take LCM]

=> x - 3/5 = +(_/19)/5 , -(_/19)/5

=> x = (3 + _/19)/5 , (3 - _/19)/5