Solve 4^2+10^2=x^2

$$4 ^ { 2 } + 10 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=2\sqrt{29}\approx 10.770329614$$

$$x=-2\sqrt{29}\approx -10.770329614$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16+10^{2}=x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$16+100=x^{2}$$

Add 16 and 100 to get 116.

$$116=x^{2}$$

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

$$x^{2}=116$$

Take the square root of both sides of the equation.

$$x=2\sqrt{29} x=-2\sqrt{29}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16+10^{2}=x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$16+100=x^{2}$$

Add 16 and 100 to get 116.

$$116=x^{2}$$

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

$$x^{2}=116$$

Subtract 116 from both sides.

$$x^{2}-116=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -116 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-116\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-116\right)}}{2}$$

Multiply -4 times -116.

$$x=\frac{0±\sqrt{464}}{2}$$

Take the square root of 464.

$$x=\frac{0±4\sqrt{29}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{29}}{2} when ± is plus.

$$x=2\sqrt{29}$$

Now solve the equation x=\frac{0±4\sqrt{29}}{2} when ± is minus.

$$x=-2\sqrt{29}$$

The equation is now solved.

$$x=2\sqrt{29} x=-2\sqrt{29}$$