Solve by Factoring x^2+15x+2 square root of x^2+15x=24

$x^{2} + 15 x + 2 \sqrt{x^{2} + 15 x} = 24$

Step 1

Subtract $24$ from both sides of the equation.

$x^{2} + 15 x + 2 \sqrt{x^{2} + 15 x} - 24 = 0$

Step 2

Factor $x$ out of $x^{2} + 15 x$ .

Factor $x$ out of $x^{2}$ .

$x^{2} + 15 x + 2 \sqrt{x \cdot x + 15 x} - 24 = 0$

Factor $x$ out of $15 x$ .

$x^{2} + 15 x + 2 \sqrt{x \cdot x + x \cdot 15} - 24 = 0$

Factor $x$ out of $x \cdot x + x \cdot 15$ .

$x^{2} + 15 x + 2 \sqrt{x (x + 15)} - 24 = 0$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 16, 1$

Step 4