Solve frac{{left(xsqrt{12*2}right)}^2}{7*2}=789/555

$$\frac{ { \left(x \sqrt{ 12 \times 2 } \right) }^{ 2 } }{ 7 \times 2 } = \frac{ 789 }{ 555 }$$

Solve for x

$$x=\frac{\sqrt{1021755}}{1110}\approx 0.910647725$$

$$x=-\frac{\sqrt{1021755}}{1110}\approx -0.910647725$$

Steps by Finding Square Root

Multiply 12 and 2 to get 24.

$$\frac{\left(x\sqrt{24}\right)^{2}}{7\times 2}=\frac{789}{555}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{\left(x\times 2\sqrt{6}\right)^{2}}{7\times 2}=\frac{789}{555}$$

Expand \left(x\times 2\sqrt{6}\right)^{2}.

$$\frac{x^{2}\times 2^{2}\left(\sqrt{6}\right)^{2}}{7\times 2}=\frac{789}{555}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{2}\times 4\left(\sqrt{6}\right)^{2}}{7\times 2}=\frac{789}{555}$$

The square of \sqrt{6} is 6.

$$\frac{x^{2}\times 4\times 6}{7\times 2}=\frac{789}{555}$$

Multiply 4 and 6 to get 24.

$$\frac{x^{2}\times 24}{7\times 2}=\frac{789}{555}$$

Multiply 7 and 2 to get 14.

$$\frac{x^{2}\times 24}{14}=\frac{789}{555}$$

Divide x^{2}\times 24 by 14 to get x^{2}\times \frac{12}{7}.

$$x^{2}\times \frac{12}{7}=\frac{789}{555}$$

Reduce the fraction \frac{789}{555} to lowest terms by extracting and canceling out 3.

$$x^{2}\times \frac{12}{7}=\frac{263}{185}$$

Multiply both sides by \frac{7}{12}, the reciprocal of \frac{12}{7}.

$$x^{2}=\frac{263}{185}\times \frac{7}{12}$$

Multiply \frac{263}{185} and \frac{7}{12} to get \frac{1841}{2220}.

$$x^{2}=\frac{1841}{2220}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{1021755}}{1110} x=-\frac{\sqrt{1021755}}{1110}$$

Steps Using the Quadratic Formula

Multiply 12 and 2 to get 24.

$$\frac{\left(x\sqrt{24}\right)^{2}}{7\times 2}=\frac{789}{555}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{\left(x\times 2\sqrt{6}\right)^{2}}{7\times 2}=\frac{789}{555}$$

Expand \left(x\times 2\sqrt{6}\right)^{2}.

$$\frac{x^{2}\times 2^{2}\left(\sqrt{6}\right)^{2}}{7\times 2}=\frac{789}{555}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{2}\times 4\left(\sqrt{6}\right)^{2}}{7\times 2}=\frac{789}{555}$$

The square of \sqrt{6} is 6.

$$\frac{x^{2}\times 4\times 6}{7\times 2}=\frac{789}{555}$$

Multiply 4 and 6 to get 24.

$$\frac{x^{2}\times 24}{7\times 2}=\frac{789}{555}$$

Multiply 7 and 2 to get 14.

$$\frac{x^{2}\times 24}{14}=\frac{789}{555}$$

Divide x^{2}\times 24 by 14 to get x^{2}\times \frac{12}{7}.

$$x^{2}\times \frac{12}{7}=\frac{789}{555}$$

Reduce the fraction \frac{789}{555} to lowest terms by extracting and canceling out 3.

$$x^{2}\times \frac{12}{7}=\frac{263}{185}$$

Subtract \frac{263}{185} from both sides.

$$x^{2}\times \frac{12}{7}-\frac{263}{185}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{12}{7}x^{2}-\frac{263}{185}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{12}{7} for a, 0 for b, and -\frac{263}{185} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{12}{7}\left(-\frac{263}{185}\right)}}{2\times \frac{12}{7}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{12}{7}\left(-\frac{263}{185}\right)}}{2\times \frac{12}{7}}$$

Multiply -4 times \frac{12}{7}.

$$x=\frac{0±\sqrt{-\frac{48}{7}\left(-\frac{263}{185}\right)}}{2\times \frac{12}{7}}$$

Multiply -\frac{48}{7} times -\frac{263}{185} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{12624}{1295}}}{2\times \frac{12}{7}}$$

Take the square root of \frac{12624}{1295}.

$$x=\frac{0±\frac{4\sqrt{1021755}}{1295}}{2\times \frac{12}{7}}$$

Multiply 2 times \frac{12}{7}.

$$x=\frac{0±\frac{4\sqrt{1021755}}{1295}}{\frac{24}{7}}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{1021755}}{1295}}{\frac{24}{7}} when ± is plus.

$$x=\frac{\sqrt{1021755}}{1110}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{1021755}}{1295}}{\frac{24}{7}} when ± is minus.

$$x=-\frac{\sqrt{1021755}}{1110}$$

The equation is now solved.

$$x=\frac{\sqrt{1021755}}{1110} x=-\frac{\sqrt{1021755}}{1110}$$