Solve (x)(x+5)=234

$$( x ) ( x + 5 ) = 234$$

Solve for x

$$x=-18$$

$$x=13$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+5.

$$x^{2}+5x=234$$

Subtract 234 from both sides.

$$x^{2}+5x-234=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 5 for b, and -234 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-234\right)}}{2}$$

Square 5.

$$x=\frac{-5±\sqrt{25-4\left(-234\right)}}{2}$$

Multiply -4 times -234.

$$x=\frac{-5±\sqrt{25+936}}{2}$$

Add 25 to 936.

$$x=\frac{-5±\sqrt{961}}{2}$$

Take the square root of 961.

$$x=\frac{-5±31}{2}$$

Now solve the equation x=\frac{-5±31}{2} when ± is plus. Add -5 to 31.

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

Divide 26 by 2.

$$x=13$$

Now solve the equation x=\frac{-5±31}{2} when ± is minus. Subtract 31 from -5.

$$x=-\frac{36}{2}$$

Divide -36 by 2.

$$x=-18$$

The equation is now solved.

$$x=13 x=-18$$

Steps for Completing the Square

Use the distributive property to multiply x by x+5.

$$x^{2}+5x=234$$

Divide 5, the coefficient of the x term, by 2 to get \frac{5}{2}. Then add the square of \frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=234+\left(\frac{5}{2}\right)^{2}$$

Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+5x+\frac{25}{4}=234+\frac{25}{4}$$

Add 234 to \frac{25}{4}.

$$x^{2}+5x+\frac{25}{4}=\frac{961}{4}$$

Factor x^{2}+5x+\frac{25}{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}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{961}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{961}{4}}$$

Simplify.

$$x+\frac{5}{2}=\frac{31}{2} x+\frac{5}{2}=-\frac{31}{2}$$

Subtract \frac{5}{2} from both sides of the equation.

$$x=13 x=-18$$