Solve 15.1+xdivx(12)=3x

$$15.1+x \div x(12)=3x$$

Solve for x

$$x = \frac{271}{30} = 9\frac{1}{30} \approx 9.033333333$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 15.1+x\times 12=3xx$$

Multiply x and x to get x^{2}.

$$x\times 15.1+x\times 12=3x^{2}$$

Combine x\times 15.1 and x\times 12 to get 27.1x.

$$27.1x=3x^{2}$$

Subtract 3x^{2} from both sides.

$$27.1x-3x^{2}=0$$

Factor out x.

$$x\left(27.1-3x\right)=0$$

To find equation solutions, solve x=0 and 27.1-3x=0.

$$x=0 x=\frac{271}{30}$$

Variable x cannot be equal to 0.

$$x=\frac{271}{30}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 15.1+x\times 12=3xx$$

Multiply x and x to get x^{2}.

$$x\times 15.1+x\times 12=3x^{2}$$

Combine x\times 15.1 and x\times 12 to get 27.1x.

$$27.1x=3x^{2}$$

Subtract 3x^{2} from both sides.

$$27.1x-3x^{2}=0$$

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.

$$-3x^{2}+27.1x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 27.1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-27.1±\sqrt{27.1^{2}}}{2\left(-3\right)}$$

Take the square root of 27.1^{2}.

$$x=\frac{-27.1±\frac{271}{10}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{-27.1±\frac{271}{10}}{-6}$$

Now solve the equation x=\frac{-27.1±\frac{271}{10}}{-6} when ± is plus. Add -27.1 to \frac{271}{10} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{-6}$$

Divide 0 by -6.

$$x=0$$

Now solve the equation x=\frac{-27.1±\frac{271}{10}}{-6} when ± is minus. Subtract \frac{271}{10} from -27.1 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{271}{5}}{-6}$$

Divide -\frac{271}{5} by -6.

$$x=\frac{271}{30}$$

The equation is now solved.

$$x=0 x=\frac{271}{30}$$

Variable x cannot be equal to 0.

$$x=\frac{271}{30}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 15.1+x\times 12=3xx$$

Multiply x and x to get x^{2}.

$$x\times 15.1+x\times 12=3x^{2}$$

Combine x\times 15.1 and x\times 12 to get 27.1x.

$$27.1x=3x^{2}$$

Subtract 3x^{2} from both sides.

$$27.1x-3x^{2}=0$$

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.

$$-3x^{2}+27.1x=0$$

Divide both sides by -3.

$$\frac{-3x^{2}+27.1x}{-3}=\frac{0}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x^{2}+\frac{27.1}{-3}x=\frac{0}{-3}$$

Divide 27.1 by -3.

$$x^{2}-\frac{271}{30}x=\frac{0}{-3}$$

Divide 0 by -3.

$$x^{2}-\frac{271}{30}x=0$$

Divide -\frac{271}{30}, the coefficient of the x term, by 2 to get -\frac{271}{60}. Then add the square of -\frac{271}{60} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{271}{30}x+\left(-\frac{271}{60}\right)^{2}=\left(-\frac{271}{60}\right)^{2}$$

Square -\frac{271}{60} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{271}{30}x+\frac{73441}{3600}=\frac{73441}{3600}$$

Factor x^{2}-\frac{271}{30}x+\frac{73441}{3600}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{271}{60}\right)^{2}=\frac{73441}{3600}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{271}{60}\right)^{2}}=\sqrt{\frac{73441}{3600}}$$

Simplify.

$$x-\frac{271}{60}=\frac{271}{60} x-\frac{271}{60}=-\frac{271}{60}$$

Add \frac{271}{60} to both sides of the equation.

$$x=\frac{271}{30} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{271}{30}$$