Solve (x+1)(x+4)=(2-(x

$$(x+1)(x+4)=(2-(x$$

Solve for x (complex solution)

$$x=\sqrt{7}-3\approx -0.354248689$$

$$x=-\left(\sqrt{7}+3\right)\approx -5.645751311$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$x^{2}+5x+4=2-x$$

Subtract 2 from both sides.

$$x^{2}+5x+4-2=-x$$

Subtract 2 from 4 to get 2.

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

Add x to both sides.

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

Combine 5x and x to get 6x.

$$x^{2}+6x+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 6.

$$x=\frac{-6±\sqrt{36-4\times 2}}{2}$$

Multiply -4 times 2.

$$x=\frac{-6±\sqrt{36-8}}{2}$$

Add 36 to -8.

$$x=\frac{-6±\sqrt{28}}{2}$$

Take the square root of 28.

$$x=\frac{-6±2\sqrt{7}}{2}$$

Now solve the equation x=\frac{-6±2\sqrt{7}}{2} when ± is plus. Add -6 to 2\sqrt{7}.

$$x=\frac{2\sqrt{7}-6}{2}$$

Divide -6+2\sqrt{7} by 2.

$$x=\sqrt{7}-3$$

Now solve the equation x=\frac{-6±2\sqrt{7}}{2} when ± is minus. Subtract 2\sqrt{7} from -6.

$$x=\frac{-2\sqrt{7}-6}{2}$$

Divide -6-2\sqrt{7} by 2.

$$x=-\sqrt{7}-3$$

The equation is now solved.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$

Steps for Completing the Square

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$x^{2}+5x+4=2-x$$

Add x to both sides.

$$x^{2}+5x+4+x=2$$

Combine 5x and x to get 6x.

$$x^{2}+6x+4=2$$

Subtract 4 from both sides.

$$x^{2}+6x=2-4$$

Subtract 4 from 2 to get -2.

$$x^{2}+6x=-2$$

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+6x+3^{2}=-2+3^{2}$$

Square 3.

$$x^{2}+6x+9=-2+9$$

Add -2 to 9.

$$x^{2}+6x+9=7$$

Factor x^{2}+6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+3\right)^{2}=7$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{7}$$

Simplify.

$$x+3=\sqrt{7} x+3=-\sqrt{7}$$

Subtract 3 from both sides of the equation.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$

Solve for x

$$x=\sqrt{7}-3\approx -0.354248689$$

$$x=-\sqrt{7}-3\approx -5.645751311$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$x^{2}+5x+4=2-x$$

Subtract 2 from both sides.

$$x^{2}+5x+4-2=-x$$

Subtract 2 from 4 to get 2.

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

Add x to both sides.

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

Combine 5x and x to get 6x.

$$x^{2}+6x+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 6.

$$x=\frac{-6±\sqrt{36-4\times 2}}{2}$$

Multiply -4 times 2.

$$x=\frac{-6±\sqrt{36-8}}{2}$$

Add 36 to -8.

$$x=\frac{-6±\sqrt{28}}{2}$$

Take the square root of 28.

$$x=\frac{-6±2\sqrt{7}}{2}$$

Now solve the equation x=\frac{-6±2\sqrt{7}}{2} when ± is plus. Add -6 to 2\sqrt{7}.

$$x=\frac{2\sqrt{7}-6}{2}$$

Divide -6+2\sqrt{7} by 2.

$$x=\sqrt{7}-3$$

Now solve the equation x=\frac{-6±2\sqrt{7}}{2} when ± is minus. Subtract 2\sqrt{7} from -6.

$$x=\frac{-2\sqrt{7}-6}{2}$$

Divide -6-2\sqrt{7} by 2.

$$x=-\sqrt{7}-3$$

The equation is now solved.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$

Steps for Completing the Square

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$x^{2}+5x+4=2-x$$

Add x to both sides.

$$x^{2}+5x+4+x=2$$

Combine 5x and x to get 6x.

$$x^{2}+6x+4=2$$

Subtract 4 from both sides.

$$x^{2}+6x=2-4$$

Subtract 4 from 2 to get -2.

$$x^{2}+6x=-2$$

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+6x+3^{2}=-2+3^{2}$$

Square 3.

$$x^{2}+6x+9=-2+9$$

Add -2 to 9.

$$x^{2}+6x+9=7$$

Factor x^{2}+6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+3\right)^{2}=7$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{7}$$

Simplify.

$$x+3=\sqrt{7} x+3=-\sqrt{7}$$

Subtract 3 from both sides of the equation.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$