Solve x^2=13^2+5^2

$$x ^ { 2 } = 13 ^ { 2 } + 5 ^ { 2 }$$

Solve for x

$$x=\sqrt{194}\approx 13.928388277$$

$$x=-\sqrt{194}\approx -13.928388277$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$x^{2}=169+5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$x^{2}=169+25$$

Add 169 and 25 to get 194.

$$x^{2}=194$$

Take the square root of both sides of the equation.

$$x=\sqrt{194} x=-\sqrt{194}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$x^{2}=169+5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$x^{2}=169+25$$

Add 169 and 25 to get 194.

$$x^{2}=194$$

Subtract 194 from both sides.

$$x^{2}-194=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -194 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-194\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-194\right)}}{2}$$

Multiply -4 times -194.

$$x=\frac{0±\sqrt{776}}{2}$$

Take the square root of 776.

$$x=\frac{0±2\sqrt{194}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{194}}{2} when ± is plus.

$$x=\sqrt{194}$$

Now solve the equation x=\frac{0±2\sqrt{194}}{2} when ± is minus.

$$x=-\sqrt{194}$$

The equation is now solved.

$$x=\sqrt{194} x=-\sqrt{194}$$