Solve (x-3)(x+5)=2

$$( x - 3 ) ( x + 5 ) = 2$$

Solve for x

$$x=3\sqrt{2}-1\approx 3.242640687$$

$$x=-3\sqrt{2}-1\approx -5.242640687$$

Steps Using the Quadratic Formula

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

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

Subtract 2 from both sides.

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

Subtract 2 from -15 to get -17.

$$x^{2}+2x-17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-17\right)}}{2}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\left(-17\right)}}{2}$$

Multiply -4 times -17.

$$x=\frac{-2±\sqrt{4+68}}{2}$$

Add 4 to 68.

$$x=\frac{-2±\sqrt{72}}{2}$$

Take the square root of 72.

$$x=\frac{-2±6\sqrt{2}}{2}$$

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

$$x=\frac{6\sqrt{2}-2}{2}$$

Divide -2+6\sqrt{2} by 2.

$$x=3\sqrt{2}-1$$

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

$$x=\frac{-6\sqrt{2}-2}{2}$$

Divide -2-6\sqrt{2} by 2.

$$x=-3\sqrt{2}-1$$

The equation is now solved.

$$x=3\sqrt{2}-1 x=-3\sqrt{2}-1$$

Steps for Completing the Square

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

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

Add 15 to both sides.

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

Add 2 and 15 to get 17.

$$x^{2}+2x=17$$

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.

$$x^{2}+2x+1^{2}=17+1^{2}$$

Square 1.

$$x^{2}+2x+1=17+1$$

Add 17 to 1.

$$x^{2}+2x+1=18$$

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}.

$$\left(x+1\right)^{2}=18$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{18}$$

Simplify.

$$x+1=3\sqrt{2} x+1=-3\sqrt{2}$$

Subtract 1 from both sides of the equation.

$$x=3\sqrt{2}-1 x=-3\sqrt{2}-1$$