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

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

Solve for x

$$x=3\sqrt{2}-2\approx 2.242640687$$

$$x=-3\sqrt{2}-2\approx -6.242640687$$

Steps Using the Quadratic Formula

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

$$x^{2}+4x-21=-7$$

Add 7 to both sides.

$$x^{2}+4x-21+7=0$$

Add -21 and 7 to get -14.

$$x^{2}+4x-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-14\right)}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-14\right)}}{2}$$

Multiply -4 times -14.

$$x=\frac{-4±\sqrt{16+56}}{2}$$

Add 16 to 56.

$$x=\frac{-4±\sqrt{72}}{2}$$

Take the square root of 72.

$$x=\frac{-4±6\sqrt{2}}{2}$$

Now solve the equation x=\frac{-4±6\sqrt{2}}{2} when ± is plus. Add -4 to 6\sqrt{2}.

$$x=\frac{6\sqrt{2}-4}{2}$$

Divide -4+6\sqrt{2} by 2.

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

Now solve the equation x=\frac{-4±6\sqrt{2}}{2} when ± is minus. Subtract 6\sqrt{2} from -4.

$$x=\frac{-6\sqrt{2}-4}{2}$$

Divide -4-6\sqrt{2} by 2.

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

The equation is now solved.

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

Steps for Completing the Square

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

$$x^{2}+4x-21=-7$$

Add 21 to both sides.

$$x^{2}+4x=-7+21$$

Add -7 and 21 to get 14.

$$x^{2}+4x=14$$

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.

$$x^{2}+4x+2^{2}=14+2^{2}$$

Square 2.

$$x^{2}+4x+4=14+4$$

Add 14 to 4.

$$x^{2}+4x+4=18$$

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}.

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

Take the square root of both sides of the equation.

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

Simplify.

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

Subtract 2 from both sides of the equation.

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