Solve sqrt{x}:(3/2)^2+(2-1/4)^2:(1/2+1/3-frac{1}{60})*2-(1-frac{1}{6})=

$$\sqrt { x } : ( \frac { 3 } { 2 } ) ^ { 2 } + ( 2 - \frac { 1 } { 4 } ) ^ { 2 } : ( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 60 } ) \times 2 - ( 1 - \frac { 1 } { 6 } ) =$$

Factor

$$\frac{4\left(\sqrt{x}+15\right)}{9}$$

Solution Steps

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{\left(2-\frac{1}{4}\right)^{2}}{\frac{1}{2}+\frac{1}{3}-\frac{1}{60}}\times 2-\left(1-\frac{1}{6}\right))$$

Subtract \frac{1}{4} from 2 to get \frac{7}{4}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{\left(\frac{7}{4}\right)^{2}}{\frac{1}{2}+\frac{1}{3}-\frac{1}{60}}\times 2-\left(1-\frac{1}{6}\right))$$

Calculate \frac{7}{4} to the power of 2 and get \frac{49}{16}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{\frac{49}{16}}{\frac{1}{2}+\frac{1}{3}-\frac{1}{60}}\times 2-\left(1-\frac{1}{6}\right))$$

Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{\frac{49}{16}}{\frac{5}{6}-\frac{1}{60}}\times 2-\left(1-\frac{1}{6}\right))$$

Subtract \frac{1}{60} from \frac{5}{6} to get \frac{49}{60}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{\frac{49}{16}}{\frac{49}{60}}\times 2-\left(1-\frac{1}{6}\right))$$

Divide \frac{49}{16} by \frac{49}{60} by multiplying \frac{49}{16} by the reciprocal of \frac{49}{60}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{49}{16}\times \frac{60}{49}\times 2-\left(1-\frac{1}{6}\right))$$

Multiply \frac{49}{16} and \frac{60}{49} to get \frac{15}{4}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{15}{4}\times 2-\left(1-\frac{1}{6}\right))$$

Multiply \frac{15}{4} and 2 to get \frac{15}{2}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{15}{2}-\left(1-\frac{1}{6}\right))$$

Subtract \frac{1}{6} from 1 to get \frac{5}{6}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{15}{2}-\frac{5}{6})$$

Subtract \frac{5}{6} from \frac{15}{2} to get \frac{20}{3}.

$$factor(\frac{\sqrt{x}}{\frac{9}{4}}+\frac{20}{3})$$

Divide \sqrt{x} by \frac{9}{4} by multiplying \sqrt{x} by the reciprocal of \frac{9}{4}.

$$factor(\frac{\sqrt{x}\times 4}{9}+\frac{20}{3})$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 3 is 9. Multiply \frac{20}{3} times \frac{3}{3}.

$$factor(\frac{\sqrt{x}\times 4}{9}+\frac{20\times 3}{9})$$

Since \frac{\sqrt{x}\times 4}{9} and \frac{20\times 3}{9} have the same denominator, add them by adding their numerators.

$$factor(\frac{\sqrt{x}\times 4+20\times 3}{9})$$

Do the multiplications in \sqrt{x}\times 4+20\times 3.

$$factor(\frac{4\sqrt{x}+60}{9})$$

Consider 4x^{\frac{1}{2}}+60. Factor out 4.

$$4\left(\sqrt{x}+15\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{4\left(\sqrt{x}+15\right)}{9}$$

Evaluate

$$\frac{4\left(\sqrt{x}+15\right)}{9}$$