Solve (x-3)(x+7)=-9

$$( x - 3 ) ( x + 7 ) = - 9$$

Solve for x

$$x=-6$$

$$x=2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-3 by x+7 and combine like terms.

$$x^{2}+4x-21=-9$$

Add 9 to both sides.

$$x^{2}+4x-21+9=0$$

Add -21 and 9 to get -12.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-12\right)}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-12\right)}}{2}$$

Multiply -4 times -12.

$$x=\frac{-4±\sqrt{16+48}}{2}$$

Add 16 to 48.

$$x=\frac{-4±\sqrt{64}}{2}$$

Take the square root of 64.

$$x=\frac{-4±8}{2}$$

Now solve the equation x=\frac{-4±8}{2} when ± is plus. Add -4 to 8.

$$x=\frac{4}{2}$$

Divide 4 by 2.

$$x=2$$

Now solve the equation x=\frac{-4±8}{2} when ± is minus. Subtract 8 from -4.

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

Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=2 x=-6$$

Steps for Completing the Square

Use the distributive property to multiply x-3 by x+7 and combine like terms.

$$x^{2}+4x-21=-9$$

Add 21 to both sides.

$$x^{2}+4x=-9+21$$

Add -9 and 21 to get 12.

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

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.

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

Square 2.

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

Add 12 to 4.

$$x^{2}+4x+4=16$$

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}.

$$\left(x+2\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{16}$$

Simplify.

$$x+2=4 x+2=-4$$

Subtract 2 from both sides of the equation.

$$x=2 x=-6$$