Solve 160=x(x+6)

$$160=x(x+6)$$

Solve for x

$$x=-16$$

$$x=10$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+6.

$$160=x^{2}+6x$$

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

$$x^{2}+6x=160$$

Subtract 160 from both sides.

$$x^{2}+6x-160=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and -160 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-160\right)}}{2}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\left(-160\right)}}{2}$$

Multiply -4 times -160.

$$x=\frac{-6±\sqrt{36+640}}{2}$$

Add 36 to 640.

$$x=\frac{-6±\sqrt{676}}{2}$$

Take the square root of 676.

$$x=\frac{-6±26}{2}$$

Now solve the equation x=\frac{-6±26}{2} when ± is plus. Add -6 to 26.

$$x=\frac{20}{2}$$

Divide 20 by 2.

$$x=10$$

Now solve the equation x=\frac{-6±26}{2} when ± is minus. Subtract 26 from -6.

$$x=-\frac{32}{2}$$

Divide -32 by 2.

$$x=-16$$

The equation is now solved.

$$x=10 x=-16$$

Steps for Completing the Square

Use the distributive property to multiply x by x+6.

$$160=x^{2}+6x$$

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

$$x^{2}+6x=160$$

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+6x+3^{2}=160+3^{2}$$

Square 3.

$$x^{2}+6x+9=160+9$$

Add 160 to 9.

$$x^{2}+6x+9=169$$

Factor x^{2}+6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+3\right)^{2}=169$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{169}$$

Simplify.

$$x+3=13 x+3=-13$$

Subtract 3 from both sides of the equation.

$$x=10 x=-16$$