Solve 15=x(x+16)

$$15=x(x+16)$$

Solve for x (complex solution)

$$x=\sqrt{79}-8\approx 0.888194417$$

$$x=-\left(\sqrt{79}+8\right)\approx -16.888194417$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+16.

$$15=x^{2}+16x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x=15$$

Subtract 15 from both sides.

$$x^{2}+16x-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-15\right)}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$x=\frac{-16±\sqrt{256+60}}{2}$$

Add 256 to 60.

$$x=\frac{-16±\sqrt{316}}{2}$$

Take the square root of 316.

$$x=\frac{-16±2\sqrt{79}}{2}$$

Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is plus. Add -16 to 2\sqrt{79}.

$$x=\frac{2\sqrt{79}-16}{2}$$

Divide -16+2\sqrt{79} by 2.

$$x=\sqrt{79}-8$$

Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is minus. Subtract 2\sqrt{79} from -16.

$$x=\frac{-2\sqrt{79}-16}{2}$$

Divide -16-2\sqrt{79} by 2.

$$x=-\sqrt{79}-8$$

The equation is now solved.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$

Steps for Completing the Square

Use the distributive property to multiply x by x+16.

$$15=x^{2}+16x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x=15$$

Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+16x+8^{2}=15+8^{2}$$

Square 8.

$$x^{2}+16x+64=15+64$$

Add 15 to 64.

$$x^{2}+16x+64=79$$

Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+8\right)^{2}=79$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{79}$$

Simplify.

$$x+8=\sqrt{79} x+8=-\sqrt{79}$$

Subtract 8 from both sides of the equation.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$

Solve for x

$$x=\sqrt{79}-8\approx 0.888194417$$

$$x=-\sqrt{79}-8\approx -16.888194417$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+16.

$$15=x^{2}+16x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x=15$$

Subtract 15 from both sides.

$$x^{2}+16x-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-15\right)}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$x=\frac{-16±\sqrt{256+60}}{2}$$

Add 256 to 60.

$$x=\frac{-16±\sqrt{316}}{2}$$

Take the square root of 316.

$$x=\frac{-16±2\sqrt{79}}{2}$$

Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is plus. Add -16 to 2\sqrt{79}.

$$x=\frac{2\sqrt{79}-16}{2}$$

Divide -16+2\sqrt{79} by 2.

$$x=\sqrt{79}-8$$

Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is minus. Subtract 2\sqrt{79} from -16.

$$x=\frac{-2\sqrt{79}-16}{2}$$

Divide -16-2\sqrt{79} by 2.

$$x=-\sqrt{79}-8$$

The equation is now solved.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$

Steps for Completing the Square

Use the distributive property to multiply x by x+16.

$$15=x^{2}+16x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x=15$$

Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+16x+8^{2}=15+8^{2}$$

Square 8.

$$x^{2}+16x+64=15+64$$

Add 15 to 64.

$$x^{2}+16x+64=79$$

Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+8\right)^{2}=79$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{79}$$

Simplify.

$$x+8=\sqrt{79} x+8=-\sqrt{79}$$

Subtract 8 from both sides of the equation.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$