Solve 1-3/4sqrt{1/2-7/10x}=-2^-1

$$1 - \frac { 3 } { 4 } \sqrt { \frac { 1 } { 2 } - \frac { 7 } { 10 } x } = - 2 ^ { - 1 }$$

Solve for x

$$x=-5$$

Steps for Solving Radical Equations

Subtract 1 from both sides of the equation.

$$-\frac{3}{4}\sqrt{-\frac{7}{10}x+\frac{1}{2}}+1-1=-\frac{1}{2}-1$$

Subtracting 1 from itself leaves 0.

$$-\frac{3}{4}\sqrt{-\frac{7}{10}x+\frac{1}{2}}=-\frac{1}{2}-1$$

Subtract 1 from -\frac{1}{2}.

$$-\frac{3}{4}\sqrt{-\frac{7}{10}x+\frac{1}{2}}=-\frac{3}{2}$$

Divide both sides of the equation by -\frac{3}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{4}\sqrt{-\frac{7}{10}x+\frac{1}{2}}}{-\frac{3}{4}}=-\frac{\frac{3}{2}}{-\frac{3}{4}}$$

Dividing by -\frac{3}{4} undoes the multiplication by -\frac{3}{4}.

$$\sqrt{-\frac{7}{10}x+\frac{1}{2}}=-\frac{\frac{3}{2}}{-\frac{3}{4}}$$

Divide -\frac{3}{2} by -\frac{3}{4} by multiplying -\frac{3}{2} by the reciprocal of -\frac{3}{4}.

$$\sqrt{-\frac{7}{10}x+\frac{1}{2}}=2$$

Square both sides of the equation.

$$-\frac{7}{10}x+\frac{1}{2}=4$$

Subtract \frac{1}{2} from both sides of the equation.

$$-\frac{7}{10}x+\frac{1}{2}-\frac{1}{2}=4-\frac{1}{2}$$

Subtracting \frac{1}{2} from itself leaves 0.

$$-\frac{7}{10}x=4-\frac{1}{2}$$

Subtract \frac{1}{2} from 4.

$$-\frac{7}{10}x=\frac{7}{2}$$

Divide both sides of the equation by -\frac{7}{10}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{7}{10}x}{-\frac{7}{10}}=\frac{\frac{7}{2}}{-\frac{7}{10}}$$

Dividing by -\frac{7}{10} undoes the multiplication by -\frac{7}{10}.

$$x=\frac{\frac{7}{2}}{-\frac{7}{10}}$$

Divide \frac{7}{2} by -\frac{7}{10} by multiplying \frac{7}{2} by the reciprocal of -\frac{7}{10}.

$$x=-5$$