Solve S^2=15^2+(12/2)^2

$$S ^ { 2 } = 15 ^ { 2 } + ( \frac { 12 } { 2 } ) ^ { 2 }$$

Solve for S

$$S=3\sqrt{29}\approx 16.155494421$$

$$S=-3\sqrt{29}\approx -16.155494421$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$S^{2}=225+\left(\frac{12}{2}\right)^{2}$$

Divide 12 by 2 to get 6.

$$S^{2}=225+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$S^{2}=225+36$$

Add 225 and 36 to get 261.

$$S^{2}=261$$

Take the square root of both sides of the equation.

$$S=3\sqrt{29} S=-3\sqrt{29}$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$S^{2}=225+\left(\frac{12}{2}\right)^{2}$$

Divide 12 by 2 to get 6.

$$S^{2}=225+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$S^{2}=225+36$$

Add 225 and 36 to get 261.

$$S^{2}=261$$

Subtract 261 from both sides.

$$S^{2}-261=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -261 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$S=\frac{0±\sqrt{0^{2}-4\left(-261\right)}}{2}$$

Square 0.

$$S=\frac{0±\sqrt{-4\left(-261\right)}}{2}$$

Multiply -4 times -261.

$$S=\frac{0±\sqrt{1044}}{2}$$

Take the square root of 1044.

$$S=\frac{0±6\sqrt{29}}{2}$$

Now solve the equation S=\frac{0±6\sqrt{29}}{2} when ± is plus.

$$S=3\sqrt{29}$$

Now solve the equation S=\frac{0±6\sqrt{29}}{2} when ± is minus.

$$S=-3\sqrt{29}$$

The equation is now solved.

$$S=3\sqrt{29} S=-3\sqrt{29}$$