Solve 5R^2+22.55^2=27.45^2

$$5 { R }^{ 2 } + { 22.55 }^{ 2 } = { 27.45 }^{ 2 }$$

Solve for R

$$R=7$$

$$R=-7$$

Steps by Finding Square Root

Calculate 22.55 to the power of 2 and get 508.5025.

$$5R^{2}+508.5025=27.45^{2}$$

Calculate 27.45 to the power of 2 and get 753.5025.

$$5R^{2}+508.5025=753.5025$$

Subtract 508.5025 from both sides.

$$5R^{2}=753.5025-508.5025$$

Subtract 508.5025 from 753.5025 to get 245.

$$5R^{2}=245$$

Divide both sides by 5.

$$R^{2}=\frac{245}{5}$$

Divide 245 by 5 to get 49.

$$R^{2}=49$$

Take the square root of both sides of the equation.

$$R=7 R=-7$$

Steps Using the Quadratic Formula

Calculate 22.55 to the power of 2 and get 508.5025.

$$5R^{2}+508.5025=27.45^{2}$$

Calculate 27.45 to the power of 2 and get 753.5025.

$$5R^{2}+508.5025=753.5025$$

Subtract 753.5025 from both sides.

$$5R^{2}+508.5025-753.5025=0$$

Subtract 753.5025 from 508.5025 to get -245.

$$5R^{2}-245=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -245 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\times 5\left(-245\right)}}{2\times 5}$$

Square 0.

$$R=\frac{0±\sqrt{-4\times 5\left(-245\right)}}{2\times 5}$$

Multiply -4 times 5.

$$R=\frac{0±\sqrt{-20\left(-245\right)}}{2\times 5}$$

Multiply -20 times -245.

$$R=\frac{0±\sqrt{4900}}{2\times 5}$$

Take the square root of 4900.

$$R=\frac{0±70}{2\times 5}$$

Multiply 2 times 5.

$$R=\frac{0±70}{10}$$

Now solve the equation R=\frac{0±70}{10} when ± is plus. Divide 70 by 10.

$$R=7$$

Now solve the equation R=\frac{0±70}{10} when ± is minus. Divide -70 by 10.

$$R=-7$$

The equation is now solved.

$$R=7 R=-7$$