Solve 12*12x+123xdiv7x=50x

$$12 \times 12x+123x \div 7x=50x$$

Solve for x

$$x = -\frac{658}{123} = -5\frac{43}{123} \approx -5.349593496$$

$$x=0$$

Steps Using Factoring

Multiply both sides of the equation by 7.

$$84\times 12x+123xx=350x$$

Multiply 84 and 12 to get 1008.

$$1008x+123xx=350x$$

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

$$1008x+123x^{2}=350x$$

Subtract 350x from both sides.

$$1008x+123x^{2}-350x=0$$

Combine 1008x and -350x to get 658x.

$$658x+123x^{2}=0$$

Factor out x.

$$x\left(658+123x\right)=0$$

To find equation solutions, solve x=0 and 658+123x=0.

$$x=0 x=-\frac{658}{123}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 7.

$$84\times 12x+123xx=350x$$

Multiply 84 and 12 to get 1008.

$$1008x+123xx=350x$$

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

$$1008x+123x^{2}=350x$$

Subtract 350x from both sides.

$$1008x+123x^{2}-350x=0$$

Combine 1008x and -350x to get 658x.

$$658x+123x^{2}=0$$

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.

$$123x^{2}+658x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 123 for a, 658 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-658±\sqrt{658^{2}}}{2\times 123}$$

Take the square root of 658^{2}.

$$x=\frac{-658±658}{2\times 123}$$

Multiply 2 times 123.

$$x=\frac{-658±658}{246}$$

Now solve the equation x=\frac{-658±658}{246} when ± is plus. Add -658 to 658.

$$x=\frac{0}{246}$$

Divide 0 by 246.

$$x=0$$

Now solve the equation x=\frac{-658±658}{246} when ± is minus. Subtract 658 from -658.

$$x=-\frac{1316}{246}$$

Reduce the fraction \frac{-1316}{246} to lowest terms by extracting and canceling out 2.

$$x=-\frac{658}{123}$$

The equation is now solved.

$$x=0 x=-\frac{658}{123}$$

Steps for Completing the Square

Multiply both sides of the equation by 7.

$$84\times 12x+123xx=350x$$

Multiply 84 and 12 to get 1008.

$$1008x+123xx=350x$$

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

$$1008x+123x^{2}=350x$$

Subtract 350x from both sides.

$$1008x+123x^{2}-350x=0$$

Combine 1008x and -350x to get 658x.

$$658x+123x^{2}=0$$

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.

$$123x^{2}+658x=0$$

Divide both sides by 123.

$$\frac{123x^{2}+658x}{123}=\frac{0}{123}$$

Dividing by 123 undoes the multiplication by 123.

$$x^{2}+\frac{658}{123}x=\frac{0}{123}$$

Divide 0 by 123.

$$x^{2}+\frac{658}{123}x=0$$

Divide \frac{658}{123}, the coefficient of the x term, by 2 to get \frac{329}{123}. Then add the square of \frac{329}{123} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{658}{123}x+\left(\frac{329}{123}\right)^{2}=\left(\frac{329}{123}\right)^{2}$$

Square \frac{329}{123} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{658}{123}x+\frac{108241}{15129}=\frac{108241}{15129}$$

Factor x^{2}+\frac{658}{123}x+\frac{108241}{15129}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{329}{123}\right)^{2}=\frac{108241}{15129}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{329}{123}\right)^{2}}=\sqrt{\frac{108241}{15129}}$$

Simplify.

$$x+\frac{329}{123}=\frac{329}{123} x+\frac{329}{123}=-\frac{329}{123}$$

Subtract \frac{329}{123} from both sides of the equation.

$$x=0 x=-\frac{658}{123}$$