Solve 13^2=4^2+x^2

$${ 13 }^{ 2 } = { 4 }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x=3\sqrt{17}\approx 12.369316877$$

$$x=-3\sqrt{17}\approx -12.369316877$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$169=4^{2}+x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$169=16+x^{2}$$

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

$$16+x^{2}=169$$

Subtract 16 from both sides.

$$x^{2}=169-16$$

Subtract 16 from 169 to get 153.

$$x^{2}=153$$

Take the square root of both sides of the equation.

$$x=3\sqrt{17} x=-3\sqrt{17}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$169=4^{2}+x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$169=16+x^{2}$$

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

$$16+x^{2}=169$$

Subtract 169 from both sides.

$$16+x^{2}-169=0$$

Subtract 169 from 16 to get -153.

$$-153+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-153=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -153 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-153\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-153\right)}}{2}$$

Multiply -4 times -153.

$$x=\frac{0±\sqrt{612}}{2}$$

Take the square root of 612.

$$x=\frac{0±6\sqrt{17}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{17}}{2} when ± is plus.

$$x=3\sqrt{17}$$

Now solve the equation x=\frac{0±6\sqrt{17}}{2} when ± is minus.

$$x=-3\sqrt{17}$$

The equation is now solved.

$$x=3\sqrt{17} x=-3\sqrt{17}$$