Solve (x+5)(2x+1)=5

$$( x + 5 ) ( 2 x + 1 ) = 5$$

Solve for x

$$x = -\frac{11}{2} = -5\frac{1}{2} = -5.5$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+5 by 2x+1 and combine like terms.

$$2x^{2}+11x+5=5$$

Subtract 5 from both sides.

$$2x^{2}+11x+5-5=0$$

Subtract 5 from 5 to get 0.

$$2x^{2}+11x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 11 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-11±\sqrt{11^{2}}}{2\times 2}$$

Take the square root of 11^{2}.

$$x=\frac{-11±11}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-11±11}{4}$$

Now solve the equation x=\frac{-11±11}{4} when ± is plus. Add -11 to 11.

$$x=\frac{0}{4}$$

Divide 0 by 4.

$$x=0$$

Now solve the equation x=\frac{-11±11}{4} when ± is minus. Subtract 11 from -11.

$$x=-\frac{22}{4}$$

Reduce the fraction \frac{-22}{4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{11}{2}$$

The equation is now solved.

$$x=0 x=-\frac{11}{2}$$

Steps for Completing the Square

Use the distributive property to multiply x+5 by 2x+1 and combine like terms.

$$2x^{2}+11x+5=5$$

Subtract 5 from both sides.

$$2x^{2}+11x=5-5$$

Subtract 5 from 5 to get 0.

$$2x^{2}+11x=0$$

Divide both sides by 2.

$$\frac{2x^{2}+11x}{2}=\frac{0}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{11}{2}x=\frac{0}{2}$$

Divide 0 by 2.

$$x^{2}+\frac{11}{2}x=0$$

Divide \frac{11}{2}, the coefficient of the x term, by 2 to get \frac{11}{4}. Then add the square of \frac{11}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{11}{2}x+\left(\frac{11}{4}\right)^{2}=\left(\frac{11}{4}\right)^{2}$$

Square \frac{11}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{11}{2}x+\frac{121}{16}=\frac{121}{16}$$

Factor x^{2}+\frac{11}{2}x+\frac{121}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{11}{4}\right)^{2}=\frac{121}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{4}\right)^{2}}=\sqrt{\frac{121}{16}}$$

Simplify.

$$x+\frac{11}{4}=\frac{11}{4} x+\frac{11}{4}=-\frac{11}{4}$$

Subtract \frac{11}{4} from both sides of the equation.

$$x=0 x=-\frac{11}{2}$$