Solve (x+1)*(x+2)=90

$$(x+1) \times (x+2)=90$$

Solve for x

$$x=-11$$

$$x=8$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+1 by x+2 and combine like terms.

$$x^{2}+3x+2=90$$

Subtract 90 from both sides.

$$x^{2}+3x+2-90=0$$

Subtract 90 from 2 to get -88.

$$x^{2}+3x-88=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 3 for b, and -88 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-88\right)}}{2}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\left(-88\right)}}{2}$$

Multiply -4 times -88.

$$x=\frac{-3±\sqrt{9+352}}{2}$$

Add 9 to 352.

$$x=\frac{-3±\sqrt{361}}{2}$$

Take the square root of 361.

$$x=\frac{-3±19}{2}$$

Now solve the equation x=\frac{-3±19}{2} when ± is plus. Add -3 to 19.

$$x=\frac{16}{2}$$

Divide 16 by 2.

$$x=8$$

Now solve the equation x=\frac{-3±19}{2} when ± is minus. Subtract 19 from -3.

$$x=-\frac{22}{2}$$

Divide -22 by 2.

$$x=-11$$

The equation is now solved.

$$x=8 x=-11$$

Steps for Completing the Square

Use the distributive property to multiply x+1 by x+2 and combine like terms.

$$x^{2}+3x+2=90$$

Subtract 2 from both sides.

$$x^{2}+3x=90-2$$

Subtract 2 from 90 to get 88.

$$x^{2}+3x=88$$

Divide 3, the coefficient of the x term, by 2 to get \frac{3}{2}. Then add the square of \frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=88+\left(\frac{3}{2}\right)^{2}$$

Square \frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+3x+\frac{9}{4}=88+\frac{9}{4}$$

Add 88 to \frac{9}{4}.

$$x^{2}+3x+\frac{9}{4}=\frac{361}{4}$$

Factor x^{2}+3x+\frac{9}{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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{361}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{361}{4}}$$

Simplify.

$$x+\frac{3}{2}=\frac{19}{2} x+\frac{3}{2}=-\frac{19}{2}$$

Subtract \frac{3}{2} from both sides of the equation.

$$x=8 x=-11$$