Solve (x+7)(x-6)=168

$$(x+7)(x-6)=168$$

Solve for x

$$x=-15$$

$$x=14$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+7 by x-6 and combine like terms.

$$x^{2}+x-42=168$$

Subtract 168 from both sides.

$$x^{2}+x-42-168=0$$

Subtract 168 from -42 to get -210.

$$x^{2}+x-210=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1 for b, and -210 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-210\right)}}{2}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\left(-210\right)}}{2}$$

Multiply -4 times -210.

$$x=\frac{-1±\sqrt{1+840}}{2}$$

Add 1 to 840.

$$x=\frac{-1±\sqrt{841}}{2}$$

Take the square root of 841.

$$x=\frac{-1±29}{2}$$

Now solve the equation x=\frac{-1±29}{2} when ± is plus. Add -1 to 29.

$$x=\frac{28}{2}$$

Divide 28 by 2.

$$x=14$$

Now solve the equation x=\frac{-1±29}{2} when ± is minus. Subtract 29 from -1.

$$x=-\frac{30}{2}$$

Divide -30 by 2.

$$x=-15$$

The equation is now solved.

$$x=14 x=-15$$

Steps for Completing the Square

Use the distributive property to multiply x+7 by x-6 and combine like terms.

$$x^{2}+x-42=168$$

Add 42 to both sides.

$$x^{2}+x=168+42$$

Add 168 and 42 to get 210.

$$x^{2}+x=210$$

Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=210+\left(\frac{1}{2}\right)^{2}$$

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+x+\frac{1}{4}=210+\frac{1}{4}$$

Add 210 to \frac{1}{4}.

$$x^{2}+x+\frac{1}{4}=\frac{841}{4}$$

Factor x^{2}+x+\frac{1}{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}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{841}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{841}{4}}$$

Simplify.

$$x+\frac{1}{2}=\frac{29}{2} x+\frac{1}{2}=-\frac{29}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$x=14 x=-15$$