Solve 7x/92x*x=96

$$\frac{ 7x }{ 92x } \times x=96$$

Solve for x

$$x = \frac{8832}{7} = 1261\frac{5}{7} \approx 1261.714285714$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 92x.

$$7xx=8832x$$

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

$$7x^{2}=8832x$$

Subtract 8832x from both sides.

$$7x^{2}-8832x=0$$

Factor out x.

$$x\left(7x-8832\right)=0$$

To find equation solutions, solve x=0 and 7x-8832=0.

$$x=0 x=\frac{8832}{7}$$

Variable x cannot be equal to 0.

$$x=\frac{8832}{7}$$

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 92x.

$$7xx=8832x$$

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

$$7x^{2}=8832x$$

Subtract 8832x from both sides.

$$7x^{2}-8832x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, -8832 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8832\right)±\sqrt{\left(-8832\right)^{2}}}{2\times 7}$$

Take the square root of \left(-8832\right)^{2}.

$$x=\frac{-\left(-8832\right)±8832}{2\times 7}$$

The opposite of -8832 is 8832.

$$x=\frac{8832±8832}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{8832±8832}{14}$$

Now solve the equation x=\frac{8832±8832}{14} when ± is plus. Add 8832 to 8832.

$$x=\frac{17664}{14}$$

Reduce the fraction \frac{17664}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{8832}{7}$$

Now solve the equation x=\frac{8832±8832}{14} when ± is minus. Subtract 8832 from 8832.

$$x=\frac{0}{14}$$

Divide 0 by 14.

$$x=0$$

The equation is now solved.

$$x=\frac{8832}{7} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{8832}{7}$$

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 92x.

$$7xx=8832x$$

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

$$7x^{2}=8832x$$

Subtract 8832x from both sides.

$$7x^{2}-8832x=0$$

Divide both sides by 7.

$$\frac{7x^{2}-8832x}{7}=\frac{0}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x^{2}-\frac{8832}{7}x=\frac{0}{7}$$

Divide 0 by 7.

$$x^{2}-\frac{8832}{7}x=0$$

Divide -\frac{8832}{7}, the coefficient of the x term, by 2 to get -\frac{4416}{7}. Then add the square of -\frac{4416}{7} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{8832}{7}x+\left(-\frac{4416}{7}\right)^{2}=\left(-\frac{4416}{7}\right)^{2}$$

Square -\frac{4416}{7} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{8832}{7}x+\frac{19501056}{49}=\frac{19501056}{49}$$

Factor x^{2}-\frac{8832}{7}x+\frac{19501056}{49}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{4416}{7}\right)^{2}=\frac{19501056}{49}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{4416}{7}\right)^{2}}=\sqrt{\frac{19501056}{49}}$$

Simplify.

$$x-\frac{4416}{7}=\frac{4416}{7} x-\frac{4416}{7}=-\frac{4416}{7}$$

Add \frac{4416}{7} to both sides of the equation.

$$x=\frac{8832}{7} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{8832}{7}$$