Solve 8=17-sqrt{2y+11}

$$8 = 17 - \sqrt { 2 y + 11 }$$

Solve for y

$$y=35$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$17-\sqrt{2y+11}=8$$

Subtract 17 from both sides.

$$-\sqrt{2y+11}=8-17$$

Subtract 17 from 8 to get -9.

$$-\sqrt{2y+11}=-9$$

Divide both sides by -1.

$$\sqrt{2y+11}=\frac{-9}{-1}$$

Fraction \frac{-9}{-1} can be simplified to 9 by removing the negative sign from both the numerator and the denominator.

$$\sqrt{2y+11}=9$$

Square both sides of the equation.

$$2y+11=81$$

Subtract 11 from both sides of the equation.

$$2y+11-11=81-11$$

Subtracting 11 from itself leaves 0.

$$2y=81-11$$

Subtract 11 from 81.

$$2y=70$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{70}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{70}{2}$$

Divide 70 by 2.

$$y=35$$