Solve [20]x/3(22+11x)=0

$$[ 20 ] \frac { x } { 3 } ( 22 + 11 x ) = 0$$

Solve for x

$$x=-2$$

$$x=0$$

Steps Using Factoring

Multiply both sides of the equation by 3.

$$20x\left(22+11x\right)=0$$

Use the distributive property to multiply 20x by 22+11x.

$$440x+220x^{2}=0$$

Factor out x.

$$x\left(440+220x\right)=0$$

To find equation solutions, solve x=0 and 440+220x=0.

$$x=0 x=-2$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3.

$$20x\left(22+11x\right)=0$$

Use the distributive property to multiply 20x by 22+11x.

$$440x+220x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$220x^{2}+440x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 220 for a, 440 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-440±\sqrt{440^{2}}}{2\times 220}$$

Take the square root of 440^{2}.

$$x=\frac{-440±440}{2\times 220}$$

Multiply 2 times 220.

$$x=\frac{-440±440}{440}$$

Now solve the equation x=\frac{-440±440}{440} when ± is plus. Add -440 to 440.

$$x=\frac{0}{440}$$

Divide 0 by 440.

$$x=0$$

Now solve the equation x=\frac{-440±440}{440} when ± is minus. Subtract 440 from -440.

$$x=-\frac{880}{440}$$

Divide -880 by 440.

$$x=-2$$

The equation is now solved.

$$x=0 x=-2$$

Steps for Completing the Square

Multiply both sides of the equation by 3.

$$20x\left(22+11x\right)=0$$

Use the distributive property to multiply 20x by 22+11x.

$$440x+220x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$220x^{2}+440x=0$$

Divide both sides by 220.

$$\frac{220x^{2}+440x}{220}=\frac{0}{220}$$

Dividing by 220 undoes the multiplication by 220.

$$x^{2}+\frac{440}{220}x=\frac{0}{220}$$

Divide 440 by 220.

$$x^{2}+2x=\frac{0}{220}$$

Divide 0 by 220.

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

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

$$x^{2}+2x+1^{2}=1^{2}$$

Square 1.

$$x^{2}+2x+1=1$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x+1=1 x+1=-1$$

Subtract 1 from both sides of the equation.

$$x=0 x=-2$$