Solve x^2+2x=68div3x

$${ x }^{ 2 } +2x=68 \div 3x$$

Solve for x

$$x = \frac{62}{3} = 20\frac{2}{3} \approx 20.666666667$$

$$x=0$$

Steps Using Factoring

Subtract \frac{68}{3}x from both sides.

$$x^{2}+2x-\frac{68}{3}x=0$$

Combine 2x and -\frac{68}{3}x to get -\frac{62}{3}x.

$$x^{2}-\frac{62}{3}x=0$$

Factor out x.

$$x\left(x-\frac{62}{3}\right)=0$$

To find equation solutions, solve x=0 and x-\frac{62}{3}=0.

$$x=0 x=\frac{62}{3}$$

Steps Using the Quadratic Formula

Subtract \frac{68}{3}x from both sides.

$$x^{2}+2x-\frac{68}{3}x=0$$

Combine 2x and -\frac{68}{3}x to get -\frac{62}{3}x.

$$x^{2}-\frac{62}{3}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -\frac{62}{3} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{62}{3}\right)±\sqrt{\left(-\frac{62}{3}\right)^{2}}}{2}$$

Take the square root of \left(-\frac{62}{3}\right)^{2}.

$$x=\frac{-\left(-\frac{62}{3}\right)±\frac{62}{3}}{2}$$

The opposite of -\frac{62}{3} is \frac{62}{3}.

$$x=\frac{\frac{62}{3}±\frac{62}{3}}{2}$$

Now solve the equation x=\frac{\frac{62}{3}±\frac{62}{3}}{2} when ± is plus. Add \frac{62}{3} to \frac{62}{3} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{124}{3}}{2}$$

Divide \frac{124}{3} by 2.

$$x=\frac{62}{3}$$

Now solve the equation x=\frac{\frac{62}{3}±\frac{62}{3}}{2} when ± is minus. Subtract \frac{62}{3} from \frac{62}{3} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=\frac{62}{3} x=0$$

Steps for Completing the Square

Subtract \frac{68}{3}x from both sides.

$$x^{2}+2x-\frac{68}{3}x=0$$

Combine 2x and -\frac{68}{3}x to get -\frac{62}{3}x.

$$x^{2}-\frac{62}{3}x=0$$

Divide -\frac{62}{3}, the coefficient of the x term, by 2 to get -\frac{31}{3}. Then add the square of -\frac{31}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{62}{3}x+\left(-\frac{31}{3}\right)^{2}=\left(-\frac{31}{3}\right)^{2}$$

Square -\frac{31}{3} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{62}{3}x+\frac{961}{9}=\frac{961}{9}$$

Factor x^{2}-\frac{62}{3}x+\frac{961}{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}.

$$\left(x-\frac{31}{3}\right)^{2}=\frac{961}{9}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{31}{3}\right)^{2}}=\sqrt{\frac{961}{9}}$$

Simplify.

$$x-\frac{31}{3}=\frac{31}{3} x-\frac{31}{3}=-\frac{31}{3}$$

Add \frac{31}{3} to both sides of the equation.

$$x=\frac{62}{3} x=0$$