Solve (5x^2+35x+20)=(2x+4)

$$( 5 x ^ { 2 } + 35 x + 20 ) = ( 2 x + 4 )$$

Solve for x

$$x=\frac{\sqrt{769}-33}{10}\approx -0.526915075$$

$$x=\frac{-\sqrt{769}-33}{10}\approx -6.073084925$$

Steps Using the Quadratic Formula

Subtract 2x from both sides.

$$5x^{2}+35x+20-2x=4$$

Combine 35x and -2x to get 33x.

$$5x^{2}+33x+20=4$$

Subtract 4 from both sides.

$$5x^{2}+33x+20-4=0$$

Subtract 4 from 20 to get 16.

$$5x^{2}+33x+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 33 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-33±\sqrt{33^{2}-4\times 5\times 16}}{2\times 5}$$

Square 33.

$$x=\frac{-33±\sqrt{1089-4\times 5\times 16}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-33±\sqrt{1089-20\times 16}}{2\times 5}$$

Multiply -20 times 16.

$$x=\frac{-33±\sqrt{1089-320}}{2\times 5}$$

Add 1089 to -320.

$$x=\frac{-33±\sqrt{769}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-33±\sqrt{769}}{10}$$

Now solve the equation x=\frac{-33±\sqrt{769}}{10} when ± is plus. Add -33 to \sqrt{769}.

$$x=\frac{\sqrt{769}-33}{10}$$

Now solve the equation x=\frac{-33±\sqrt{769}}{10} when ± is minus. Subtract \sqrt{769} from -33.

$$x=\frac{-\sqrt{769}-33}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{769}-33}{10} x=\frac{-\sqrt{769}-33}{10}$$

Steps for Completing the Square

Subtract 2x from both sides.

$$5x^{2}+35x+20-2x=4$$

Combine 35x and -2x to get 33x.

$$5x^{2}+33x+20=4$$

Subtract 20 from both sides.

$$5x^{2}+33x=4-20$$

Subtract 20 from 4 to get -16.

$$5x^{2}+33x=-16$$

Divide both sides by 5.

$$\frac{5x^{2}+33x}{5}=-\frac{16}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\frac{33}{5}x=-\frac{16}{5}$$

Divide \frac{33}{5}, the coefficient of the x term, by 2 to get \frac{33}{10}. Then add the square of \frac{33}{10} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{33}{5}x+\left(\frac{33}{10}\right)^{2}=-\frac{16}{5}+\left(\frac{33}{10}\right)^{2}$$

Square \frac{33}{10} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{33}{5}x+\frac{1089}{100}=-\frac{16}{5}+\frac{1089}{100}$$

Add -\frac{16}{5} to \frac{1089}{100} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{33}{5}x+\frac{1089}{100}=\frac{769}{100}$$

Factor x^{2}+\frac{33}{5}x+\frac{1089}{100}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{33}{10}\right)^{2}=\frac{769}{100}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{33}{10}\right)^{2}}=\sqrt{\frac{769}{100}}$$

Simplify.

$$x+\frac{33}{10}=\frac{\sqrt{769}}{10} x+\frac{33}{10}=-\frac{\sqrt{769}}{10}$$

Subtract \frac{33}{10} from both sides of the equation.

$$x=\frac{\sqrt{769}-33}{10} x=\frac{-\sqrt{769}-33}{10}$$