Solve x=152/14*64/x

$$x = \frac { 152 } { 14 } \times \frac { 64 } { x }$$

Solve for x

$$x = \frac{16 \sqrt{133}}{7} \approx 26.360143074$$

$$x = -\frac{16 \sqrt{133}}{7} \approx -26.360143074$$

Steps by Finding Square Root

Reduce the fraction \frac{152}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{76}{7}\times \frac{64}{x}$$

Multiply \frac{76}{7} times \frac{64}{x} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{76\times 64}{7x}$$

Multiply 76 and 64 to get 4864.

$$x=\frac{4864}{7x}$$

Subtract \frac{4864}{7x} from both sides.

$$x-\frac{4864}{7x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{7x}{7x}.

$$\frac{x\times 7x}{7x}-\frac{4864}{7x}=0$$

Since \frac{x\times 7x}{7x} and \frac{4864}{7x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 7x-4864}{7x}=0$$

Do the multiplications in x\times 7x-4864.

$$\frac{7x^{2}-4864}{7x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7x.

$$7x^{2}-4864=0$$

Add 4864 to both sides. Anything plus zero gives itself.

$$7x^{2}=4864$$

Divide both sides by 7.

$$x^{2}=\frac{4864}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{16\sqrt{133}}{7} x=-\frac{16\sqrt{133}}{7}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{152}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{76}{7}\times \frac{64}{x}$$

Multiply \frac{76}{7} times \frac{64}{x} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{76\times 64}{7x}$$

Multiply 76 and 64 to get 4864.

$$x=\frac{4864}{7x}$$

Subtract \frac{4864}{7x} from both sides.

$$x-\frac{4864}{7x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{7x}{7x}.

$$\frac{x\times 7x}{7x}-\frac{4864}{7x}=0$$

Since \frac{x\times 7x}{7x} and \frac{4864}{7x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 7x-4864}{7x}=0$$

Do the multiplications in x\times 7x-4864.

$$\frac{7x^{2}-4864}{7x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7x.

$$7x^{2}-4864=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -4864 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-4864\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-4864\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-4864\right)}}{2\times 7}$$

Multiply -28 times -4864.

$$x=\frac{0±\sqrt{136192}}{2\times 7}$$

Take the square root of 136192.

$$x=\frac{0±32\sqrt{133}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±32\sqrt{133}}{14}$$

Now solve the equation x=\frac{0±32\sqrt{133}}{14} when ± is plus.

$$x=\frac{16\sqrt{133}}{7}$$

Now solve the equation x=\frac{0±32\sqrt{133}}{14} when ± is minus.

$$x=-\frac{16\sqrt{133}}{7}$$

The equation is now solved.

$$x=\frac{16\sqrt{133}}{7} x=-\frac{16\sqrt{133}}{7}$$