Solve 5^2+6^2=x^2

$$5 ^ { 2 } + 6 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=\sqrt{61}\approx 7.810249676$$

$$x=-\sqrt{61}\approx -7.810249676$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25+6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$25+36=x^{2}$$

Add 25 and 36 to get 61.

$$61=x^{2}$$

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

$$x^{2}=61$$

Take the square root of both sides of the equation.

$$x=\sqrt{61} x=-\sqrt{61}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25+6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$25+36=x^{2}$$

Add 25 and 36 to get 61.

$$61=x^{2}$$

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

$$x^{2}=61$$

Subtract 61 from both sides.

$$x^{2}-61=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -61 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-61\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-61\right)}}{2}$$

Multiply -4 times -61.

$$x=\frac{0±\sqrt{244}}{2}$$

Take the square root of 244.

$$x=\frac{0±2\sqrt{61}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{61}}{2} when ± is plus.

$$x=\sqrt{61}$$

Now solve the equation x=\frac{0±2\sqrt{61}}{2} when ± is minus.

$$x=-\sqrt{61}$$

The equation is now solved.

$$x=\sqrt{61} x=-\sqrt{61}$$