Question

Explain how you could use the formula

(x + a)2 = x2 + 2ax + a2

to solve the quadratic equation

x2 + 5x - 24 = 0.

Answer 1

Answer:

$x = \sqrt{24} - \frac{5}{2}\\ x =- \sqrt{24} - \frac{5}{2}$

Step-by-step explanation:

$x^2+5x-24=0\\x^2+2.x.\frac{5}{2} + \frac{5^2}{2^2}-\frac{5^2}{2^2}=24\\ \\(x+\frac{5}{2})^2=24\\ x+\frac{5}{2} = \sqrt{24}\\ x+\frac{5}{2} = -\sqrt{24}$