Solve 5^2+15^2=(2r)^2

$$5 ^ { 2 } + 15 ^ { 2 } = ( 2 r ) ^ { 2 }$$

Solve for r

$$r = \frac{5 \sqrt{10}}{2} \approx 7.90569415$$

$$r = -\frac{5 \sqrt{10}}{2} \approx -7.90569415$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25+15^{2}=\left(2r\right)^{2}$$

Calculate 15 to the power of 2 and get 225.

$$25+225=\left(2r\right)^{2}$$

Add 25 and 225 to get 250.

$$250=\left(2r\right)^{2}$$

Expand \left(2r\right)^{2}.

$$250=2^{2}r^{2}$$

Calculate 2 to the power of 2 and get 4.

$$250=4r^{2}$$

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

$$4r^{2}=250$$

Divide both sides by 4.

$$r^{2}=\frac{250}{4}$$

Reduce the fraction \frac{250}{4} to lowest terms by extracting and canceling out 2.

$$r^{2}=\frac{125}{2}$$

Take the square root of both sides of the equation.

$$r=\frac{5\sqrt{10}}{2} r=-\frac{5\sqrt{10}}{2}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25+15^{2}=\left(2r\right)^{2}$$

Calculate 15 to the power of 2 and get 225.

$$25+225=\left(2r\right)^{2}$$

Add 25 and 225 to get 250.

$$250=\left(2r\right)^{2}$$

Expand \left(2r\right)^{2}.

$$250=2^{2}r^{2}$$

Calculate 2 to the power of 2 and get 4.

$$250=4r^{2}$$

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

$$4r^{2}=250$$

Subtract 250 from both sides.

$$4r^{2}-250=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -250 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 4\left(-250\right)}}{2\times 4}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 4\left(-250\right)}}{2\times 4}$$

Multiply -4 times 4.

$$r=\frac{0±\sqrt{-16\left(-250\right)}}{2\times 4}$$

Multiply -16 times -250.

$$r=\frac{0±\sqrt{4000}}{2\times 4}$$

Take the square root of 4000.

$$r=\frac{0±20\sqrt{10}}{2\times 4}$$

Multiply 2 times 4.

$$r=\frac{0±20\sqrt{10}}{8}$$

Now solve the equation r=\frac{0±20\sqrt{10}}{8} when ± is plus.

$$r=\frac{5\sqrt{10}}{2}$$

Now solve the equation r=\frac{0±20\sqrt{10}}{8} when ± is minus.

$$r=-\frac{5\sqrt{10}}{2}$$

The equation is now solved.

$$r=\frac{5\sqrt{10}}{2} r=-\frac{5\sqrt{10}}{2}$$