Find the roots of $$\sqrt{2x + 9} + x = 13$$​.

Correct option is C

Given:

​$$\text{Equation to solve:} \\\ \\\sqrt{2x + 9} + x = 13 \\ \\$$​​

Formula Used:

The quadratic formula for the equation $$a x^2 + b x + c = 0$$​​

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$​​

Solution:

​$$\sqrt{2x + 9} = 13 - x \\\ \\(\sqrt{2x + 9})^2 = (13 - x)^2 \\\ \\2x + 9 = 169 - 26x + x^2 \\\ \\x^2 - 28x + 160 = 0 \\\ \ \\\text{Using the formla} \\ \ \\x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\\ \\\text{For } a = 1, b = -28, c = 160, \text{ we get:} \\\ \\x = \frac{-(-28) \pm \sqrt{(-28)^2 - 4(1)(160)}}{2(1)} \\\ \\x = \frac{28 \pm \sqrt{784 - 640}}{2} \\\ \\x = \frac{28 \pm \sqrt{144}}{2} \\\ \\x = \frac{28 \pm 12}{2} \\\ \\x = \frac{28 + 12}{2} = 20, \quad \text{or} \quad x = \frac{28 - 12}{2} = 8$$ 

Thus, the roots are 20, 8.