Solve 160=14*x+(13+x)x

$$160=14 \times x+(13+x)x$$

Solve for x

$$x=-32$$

$$x=5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 13+x by x.

$$160=14x+13x+x^{2}$$

Combine 14x and 13x to get 27x.

$$160=27x+x^{2}$$

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

$$27x+x^{2}=160$$

Subtract 160 from both sides.

$$27x+x^{2}-160=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}+27x-160=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 27 for b, and -160 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-27±\sqrt{27^{2}-4\left(-160\right)}}{2}$$

Square 27.

$$x=\frac{-27±\sqrt{729-4\left(-160\right)}}{2}$$

Multiply -4 times -160.

$$x=\frac{-27±\sqrt{729+640}}{2}$$

Add 729 to 640.

$$x=\frac{-27±\sqrt{1369}}{2}$$

Take the square root of 1369.

$$x=\frac{-27±37}{2}$$

Now solve the equation x=\frac{-27±37}{2} when ± is plus. Add -27 to 37.

$$x=\frac{10}{2}$$

Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{-27±37}{2} when ± is minus. Subtract 37 from -27.

$$x=-\frac{64}{2}$$

Divide -64 by 2.

$$x=-32$$

The equation is now solved.

$$x=5 x=-32$$

Steps for Completing the Square

Use the distributive property to multiply 13+x by x.

$$160=14x+13x+x^{2}$$

Combine 14x and 13x to get 27x.

$$160=27x+x^{2}$$

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

$$27x+x^{2}=160$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}+27x=160$$

Divide 27, the coefficient of the x term, by 2 to get \frac{27}{2}. Then add the square of \frac{27}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+27x+\left(\frac{27}{2}\right)^{2}=160+\left(\frac{27}{2}\right)^{2}$$

Square \frac{27}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+27x+\frac{729}{4}=160+\frac{729}{4}$$

Add 160 to \frac{729}{4}.

$$x^{2}+27x+\frac{729}{4}=\frac{1369}{4}$$

Factor x^{2}+27x+\frac{729}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{27}{2}\right)^{2}=\frac{1369}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{27}{2}\right)^{2}}=\sqrt{\frac{1369}{4}}$$

Simplify.

$$x+\frac{27}{2}=\frac{37}{2} x+\frac{27}{2}=-\frac{37}{2}$$

Subtract \frac{27}{2} from both sides of the equation.

$$x=5 x=-32$$