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

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

By formula,

$\Rightarrow x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[1em] \Rightarrow x = \dfrac{-(-9) \pm \sqrt{(-9)^2 - 4(1)(1)}}{2(1)} \\[1em] \Rightarrow x = \dfrac{9 \pm \sqrt{81 - 4}}{2} \\[1em] \Rightarrow x = \dfrac{9 \pm \sqrt{77}}{2} \\[1em] \Rightarrow x = \dfrac{9 \pm 8.775}{2} \\[1em] \Rightarrow x = \dfrac{9 + 8.775}{2} \text{ or } \dfrac{9 - 8.775}{2} \\[1em] \Rightarrow x = \dfrac{17.775}{2} \text{ or } \dfrac{0.225}{2} \\[1em] \Rightarrow x = 8.8875 \text{ or } 0.1125 \\[1em] \Rightarrow x = 8.89 \text{ or } 0.113$

Hence, x = 8.89 or 0.113.