Question

Solve the quadratic equation (x − 2)² − 5x − 3 = 0 and give your answer correct to 3 significant figures.

Answer 1

Given: (x − 2)² − 5x − 3 = 0

⇒ x² − 4x + 4 − 5x − 3 = 0

⇒ x² − 9x + 1 = 0

Comparing x² − 9x + 1 = 0 with ax² + bx + c = 0, we get:

a = 1, b = −9 and c = 1

Formula: x = `(-b ± sqrt((b^2) - 4ac))/(2a)`

⇒ `x = (-(-9) ± sqrt((-9)^2 - 4(1)(1)))/(2(1))`

⇒ `x = (9 ± sqrt(81 - 4))/2`

⇒ `x = (9 ± sqrt77)/2`

⇒ `x = (9 ± 8.775)/2`

⇒ `x = (9 + 8.775)/2 or (9 - 8.775)/2`

⇒ `x = (17.775)/2 or (025575)/2`

⇒ x = 8.8875 or 0.1125

⇒ x = 8.89 or 0.113

Hence, x = 8.89 or 0.113.