Solve (x+4)(x)=117

$$( x + 4 ) ( x ) = 117$$

Solve for x

$$x=-13$$

$$x=9$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+4 by x.

$$x^{2}+4x=117$$

Subtract 117 from both sides.

$$x^{2}+4x-117=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -117 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-117\right)}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-117\right)}}{2}$$

Multiply -4 times -117.

$$x=\frac{-4±\sqrt{16+468}}{2}$$

Add 16 to 468.

$$x=\frac{-4±\sqrt{484}}{2}$$

Take the square root of 484.

$$x=\frac{-4±22}{2}$$

Now solve the equation x=\frac{-4±22}{2} when ± is plus. Add -4 to 22.

$$x=\frac{18}{2}$$

Divide 18 by 2.

$$x=9$$

Now solve the equation x=\frac{-4±22}{2} when ± is minus. Subtract 22 from -4.

$$x=-\frac{26}{2}$$

Divide -26 by 2.

$$x=-13$$

The equation is now solved.

$$x=9 x=-13$$

Steps for Completing the Square

Use the distributive property to multiply x+4 by x.

$$x^{2}+4x=117$$

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.

$$x^{2}+4x+2^{2}=117+2^{2}$$

Square 2.

$$x^{2}+4x+4=117+4$$

Add 117 to 4.

$$x^{2}+4x+4=121$$

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}.

$$\left(x+2\right)^{2}=121$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{121}$$

Simplify.

$$x+2=11 x+2=-11$$

Subtract 2 from both sides of the equation.

$$x=9 x=-13$$