Solve (x+2)(x-6)=3

$$( x + 2 ) ( x - 6 ) = 3$$

Solve for x

$$x=\sqrt{19}+2\approx 6.358898944$$

$$x=2-\sqrt{19}\approx -2.358898944$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+2 by x-6 and combine like terms.

$$x^{2}-4x-12=3$$

Subtract 3 from both sides.

$$x^{2}-4x-12-3=0$$

Subtract 3 from -12 to get -15.

$$x^{2}-4x-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-15\right)}}{2}$$

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$x=\frac{-\left(-4\right)±\sqrt{16+60}}{2}$$

Add 16 to 60.

$$x=\frac{-\left(-4\right)±\sqrt{76}}{2}$$

Take the square root of 76.

$$x=\frac{-\left(-4\right)±2\sqrt{19}}{2}$$

The opposite of -4 is 4.

$$x=\frac{4±2\sqrt{19}}{2}$$

Now solve the equation x=\frac{4±2\sqrt{19}}{2} when ± is plus. Add 4 to 2\sqrt{19}.

$$x=\frac{2\sqrt{19}+4}{2}$$

Divide 4+2\sqrt{19} by 2.

$$x=\sqrt{19}+2$$

Now solve the equation x=\frac{4±2\sqrt{19}}{2} when ± is minus. Subtract 2\sqrt{19} from 4.

$$x=\frac{4-2\sqrt{19}}{2}$$

Divide 4-2\sqrt{19} by 2.

$$x=2-\sqrt{19}$$

The equation is now solved.

$$x=\sqrt{19}+2 x=2-\sqrt{19}$$

Steps for Completing the Square

Use the distributive property to multiply x+2 by x-6 and combine like terms.

$$x^{2}-4x-12=3$$

Add 12 to both sides.

$$x^{2}-4x=3+12$$

Add 3 and 12 to get 15.

$$x^{2}-4x=15$$

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-4x+\left(-2\right)^{2}=15+\left(-2\right)^{2}$$

Square -2.

$$x^{2}-4x+4=15+4$$

Add 15 to 4.

$$x^{2}-4x+4=19$$

Factor x^{2}-4x+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}.

$$\left(x-2\right)^{2}=19$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{19}$$

Simplify.

$$x-2=\sqrt{19} x-2=-\sqrt{19}$$

Add 2 to both sides of the equation.

$$x=\sqrt{19}+2 x=2-\sqrt{19}$$