Solve (sqrt{a^2+25})^2=466^2

$$( \sqrt { a ^ { 2 } + 25 } ) ^ { 2 } = 466 ^ { 2 }$$

Solve for a

$$a=\sqrt{217131}\approx 465.973175194$$

$$a=-\sqrt{217131}\approx -465.973175194$$

Steps by Finding Square Root

Calculate \sqrt{a^{2}+25} to the power of 2 and get a^{2}+25.

$$a^{2}+25=466^{2}$$

Calculate 466 to the power of 2 and get 217156.

$$a^{2}+25=217156$$

Subtract 25 from both sides.

$$a^{2}=217156-25$$

Subtract 25 from 217156 to get 217131.

$$a^{2}=217131$$

Take the square root of both sides of the equation.

$$a=\sqrt{217131} a=-\sqrt{217131}$$

Steps Using the Quadratic Formula

Calculate \sqrt{a^{2}+25} to the power of 2 and get a^{2}+25.

$$a^{2}+25=466^{2}$$

Calculate 466 to the power of 2 and get 217156.

$$a^{2}+25=217156$$

Subtract 217156 from both sides.

$$a^{2}[phone]=0$$

Subtract 217156 from 25 to get -217131.

$$a^{2}-217131=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -217131 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-217131\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-217131\right)}}{2}$$

Multiply -4 times -217131.

$$a=\frac{0±\sqrt{868524}}{2}$$

Take the square root of 868524.

$$a=\frac{0±2\sqrt{217131}}{2}$$

Now solve the equation a=\frac{0±2\sqrt{217131}}{2} when ± is plus.

$$a=\sqrt{217131}$$

Now solve the equation a=\frac{0±2\sqrt{217131}}{2} when ± is minus.

$$a=-\sqrt{217131}$$

The equation is now solved.

$$a=\sqrt{217131} a=-\sqrt{217131}$$