Solve (x+15)(x+5)=96

$$( x + 15 ) ( x + 5 ) = 96$$

Solve for x

$$x=-21$$

$$x=1$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+15 by x+5 and combine like terms.

$$x^{2}+20x+75=96$$

Subtract 96 from both sides.

$$x^{2}+20x+75-96=0$$

Subtract 96 from 75 to get -21.

$$x^{2}+20x-21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 20 for b, and -21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-21\right)}}{2}$$

Square 20.

$$x=\frac{-20±\sqrt{400-4\left(-21\right)}}{2}$$

Multiply -4 times -21.

$$x=\frac{-20±\sqrt{400+84}}{2}$$

Add 400 to 84.

$$x=\frac{-20±\sqrt{484}}{2}$$

Take the square root of 484.

$$x=\frac{-20±22}{2}$$

Now solve the equation x=\frac{-20±22}{2} when ± is plus. Add -20 to 22.

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

Divide 2 by 2.

$$x=1$$

Now solve the equation x=\frac{-20±22}{2} when ± is minus. Subtract 22 from -20.

$$x=-\frac{42}{2}$$

Divide -42 by 2.

$$x=-21$$

The equation is now solved.

$$x=1 x=-21$$

Steps for Completing the Square

Use the distributive property to multiply x+15 by x+5 and combine like terms.

$$x^{2}+20x+75=96$$

Subtract 75 from both sides.

$$x^{2}+20x=96-75$$

Subtract 75 from 96 to get 21.

$$x^{2}+20x=21$$

Divide 20, the coefficient of the x term, by 2 to get 10. Then add the square of 10 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+20x+10^{2}=21+10^{2}$$

Square 10.

$$x^{2}+20x+100=21+100$$

Add 21 to 100.

$$x^{2}+20x+100=121$$

Factor x^{2}+20x+100. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+10\right)^{2}=121$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{121}$$

Simplify.

$$x+10=11 x+10=-11$$

Subtract 10 from both sides of the equation.

$$x=1 x=-21$$