Solve S_1^2=93-25^2/8/8

$$S _ { 1 } ^ { 2 } = \frac { 93 - \frac { 25 ^ { 2 } } { 8 } } { 8 }$$

Solve for S_1

$$S_{1} = \frac{\sqrt{119}}{8} \approx 1.363589014$$

$$S_{1} = -\frac{\sqrt{119}}{8} \approx -1.363589014$$

Steps by Finding Square Root

Multiply both sides of the equation by 8.

$$8S_{1}^{2}=93-\frac{25^{2}}{8}$$

Calculate 25 to the power of 2 and get 625.

$$8S_{1}^{2}=93-\frac{625}{8}$$

Subtract \frac{625}{8} from 93 to get \frac{119}{8}.

$$8S_{1}^{2}=\frac{119}{8}$$

Divide both sides by 8.

$$S_{1}^{2}=\frac{\frac{119}{8}}{8}$$

Express \frac{\frac{119}{8}}{8} as a single fraction.

$$S_{1}^{2}=\frac{119}{8\times 8}$$

Multiply 8 and 8 to get 64.

$$S_{1}^{2}=\frac{119}{64}$$

Take the square root of both sides of the equation.

$$S_{1}=\frac{\sqrt{119}}{8} S_{1}=-\frac{\sqrt{119}}{8}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 8.

$$8S_{1}^{2}=93-\frac{25^{2}}{8}$$

Calculate 25 to the power of 2 and get 625.

$$8S_{1}^{2}=93-\frac{625}{8}$$

Subtract \frac{625}{8} from 93 to get \frac{119}{8}.

$$8S_{1}^{2}=\frac{119}{8}$$

Subtract \frac{119}{8} from both sides.

$$8S_{1}^{2}-\frac{119}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -\frac{119}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$S_{1}=\frac{0±\sqrt{0^{2}-4\times 8\left(-\frac{119}{8}\right)}}{2\times 8}$$

Square 0.

$$S_{1}=\frac{0±\sqrt{-4\times 8\left(-\frac{119}{8}\right)}}{2\times 8}$$

Multiply -4 times 8.

$$S_{1}=\frac{0±\sqrt{-32\left(-\frac{119}{8}\right)}}{2\times 8}$$

Multiply -32 times -\frac{119}{8}.

$$S_{1}=\frac{0±\sqrt{476}}{2\times 8}$$

Take the square root of 476.

$$S_{1}=\frac{0±2\sqrt{119}}{2\times 8}$$

Multiply 2 times 8.

$$S_{1}=\frac{0±2\sqrt{119}}{16}$$

Now solve the equation S_{1}=\frac{0±2\sqrt{119}}{16} when ± is plus.

$$S_{1}=\frac{\sqrt{119}}{8}$$

Now solve the equation S_{1}=\frac{0±2\sqrt{119}}{16} when ± is minus.

$$S_{1}=-\frac{\sqrt{119}}{8}$$

The equation is now solved.

$$S_{1}=\frac{\sqrt{119}}{8} S_{1}=-\frac{\sqrt{119}}{8}$$