Precalculus Examples

$x^{2} + 15 x + \sqrt{x^{2} + 15 x} = 20$

Step 1

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

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Step 1.1

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

$x^{2} + 15 x + \sqrt{x \cdot x + 15 x} = 20$

Step 1.2

Factor $x$ out of $15 x$ .

$x^{2} + 15 x + \sqrt{x \cdot x + x \cdot 15} = 20$

Step 1.3

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

$x^{2} + 15 x + \sqrt{x (x + 15)} = 20$

Step 2

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

$x \approx - 16, 1$

Step 3