Solve (x-5)(x+3)=9

$$( x - 5 ) ( x + 3 ) = 9$$

Solve for x

$$x=-4$$

$$x=6$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-5 by x+3 and combine like terms.

$$x^{2}-2x-15=9$$

Subtract 9 from both sides.

$$x^{2}-2x-15-9=0$$

Subtract 9 from -15 to get -24.

$$x^{2}-2x-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -2 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-24\right)}}{2}$$

Square -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-24\right)}}{2}$$

Multiply -4 times -24.

$$x=\frac{-\left(-2\right)±\sqrt{4+96}}{2}$$

Add 4 to 96.

$$x=\frac{-\left(-2\right)±\sqrt{100}}{2}$$

Take the square root of 100.

$$x=\frac{-\left(-2\right)±10}{2}$$

The opposite of -2 is 2.

$$x=\frac{2±10}{2}$$

Now solve the equation x=\frac{2±10}{2} when ± is plus. Add 2 to 10.

$$x=\frac{12}{2}$$

Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{2±10}{2} when ± is minus. Subtract 10 from 2.

$$x=-\frac{8}{2}$$

Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=6 x=-4$$

Steps for Completing the Square

Use the distributive property to multiply x-5 by x+3 and combine like terms.

$$x^{2}-2x-15=9$$

Add 15 to both sides.

$$x^{2}-2x=9+15$$

Add 9 and 15 to get 24.

$$x^{2}-2x=24$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-2x+1=24+1$$

Add 24 to 1.

$$x^{2}-2x+1=25$$

Factor x^{2}-2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-1\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{25}$$

Simplify.

$$x-1=5 x-1=-5$$

Add 1 to both sides of the equation.

$$x=6 x=-4$$