Solve for x x^2-8y=121.5

$x^{2} - 8 y = 121.5$

Add $8 y$ to both sides of the equation.

$x^{2} = 121.5 + 8 y$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{121.5 + 8 y}$

Simplify $\pm \sqrt{121.5 + 8 y}$ .

Factor $0.5$ out of $121.5 + 8 y$ .

Factor $0.5$ out of $121.5$ .

$x = \pm \sqrt{0.5 (243) + 8 y}$

Factor $0.5$ out of $8 y$ .

$x = \pm \sqrt{0.5 (243) + 0.5 (16 y)}$

Factor $0.5$ out of $0.5 (243) + 0.5 (16 y)$ .

$x = \pm \sqrt{0.5 (243 + 16 y)}$

Rewrite $0.5 (243 + 16 y)$ as ${({0.84089641}^{2})}^{2} (243 + 16 y)$ .

Rewrite $0.5$ as ${0.70710678}^{2}$ .

$x = \pm \sqrt{{0.70710678}^{2} (243 + 16 y)}$

Rewrite $0.70710678$ as ${0.84089641}^{2}$ .

$x = \pm \sqrt{{({0.84089641}^{2})}^{2} (243 + 16 y)}$

Pull terms out from under the radical.

$x = \pm {0.84089641}^{2} \sqrt{243 + 16 y}$

Raise $0.84089641$ to the power of $2$ .

$x = \pm 0.70710678 \sqrt{243 + 16 y}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 0.70710678 \sqrt{243 + 16 y}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 0.70710678 \sqrt{243 + 16 y}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 0.70710678 \sqrt{243 + 16 y}$

$x = - 0.70710678 \sqrt{243 + 16 y}$

$x = 0.70710678 \sqrt{243 + 16 y}$

$x = - 0.70710678 \sqrt{243 + 16 y}$