Solve 4^2+6^2=x^2

$$4 ^ { 2 } + 6 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=2\sqrt{13}\approx 7.211102551$$

$$x=-2\sqrt{13}\approx -7.211102551$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16+6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16+36=x^{2}$$

Add 16 and 36 to get 52.

$$52=x^{2}$$

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

$$x^{2}=52$$

Take the square root of both sides of the equation.

$$x=2\sqrt{13} x=-2\sqrt{13}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16+6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16+36=x^{2}$$

Add 16 and 36 to get 52.

$$52=x^{2}$$

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

$$x^{2}=52$$

Subtract 52 from both sides.

$$x^{2}-52=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -52 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-52\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-52\right)}}{2}$$

Multiply -4 times -52.

$$x=\frac{0±\sqrt{208}}{2}$$

Take the square root of 208.

$$x=\frac{0±4\sqrt{13}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{13}}{2} when ± is plus.

$$x=2\sqrt{13}$$

Now solve the equation x=\frac{0±4\sqrt{13}}{2} when ± is minus.

$$x=-2\sqrt{13}$$

The equation is now solved.

$$x=2\sqrt{13} x=-2\sqrt{13}$$