Solve 2(-1/4)=1-sqrt{2-(-1/4)}

$$2 ( - \frac { 1 } { 4 } ) = 1 - \sqrt { 2 - ( - \frac { 1 } { 4 } ) }$$

Verify

Solution Steps

Express 2\left(-\frac{1}{4}\right) as a single fraction.

$$\frac{2\left(-1\right)}{4}=1-\sqrt{2-\left(-\frac{1}{4}\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{-2}{4}=1-\sqrt{2-\left(-\frac{1}{4}\right)}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}=1-\sqrt{2-\left(-\frac{1}{4}\right)}$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$-\frac{1}{2}=1-\sqrt{2+\frac{1}{4}}$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{1}{2}=1-\sqrt{\frac{8}{4}+\frac{1}{4}}$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}=1-\sqrt{\frac{8+1}{4}}$$

Add 8 and 1 to get 9.

$$-\frac{1}{2}=1-\sqrt{\frac{9}{4}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$-\frac{1}{2}=1-\frac{3}{2}$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{1}{2}=\frac{2}{2}-\frac{3}{2}$$

Since \frac{2}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}=\frac{2-3}{2}$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{2}=-\frac{1}{2}$$

Compare -\frac{1}{2} and -\frac{1}{2}.

$$\text{true}$$