Solve x^2=14^2+4^2

$${ x }^{ 2 } = { 14 }^{ 2 } + { 4 }^{ 2 }$$

Solve for x

$$x=2\sqrt{53}\approx 14.560219779$$

$$x=-2\sqrt{53}\approx -14.560219779$$

Steps by Finding Square Root

Calculate 14 to the power of 2 and get 196.

$$x^{2}=196+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=196+16$$

Add 196 and 16 to get 212.

$$x^{2}=212$$

Take the square root of both sides of the equation.

$$x=2\sqrt{53} x=-2\sqrt{53}$$

Steps Using the Quadratic Formula

Calculate 14 to the power of 2 and get 196.

$$x^{2}=196+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=196+16$$

Add 196 and 16 to get 212.

$$x^{2}=212$$

Subtract 212 from both sides.

$$x^{2}-212=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -212 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-212\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-212\right)}}{2}$$

Multiply -4 times -212.

$$x=\frac{0±\sqrt{848}}{2}$$

Take the square root of 848.

$$x=\frac{0±4\sqrt{53}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{53}}{2} when ± is plus.

$$x=2\sqrt{53}$$

Now solve the equation x=\frac{0±4\sqrt{53}}{2} when ± is minus.

$$x=-2\sqrt{53}$$

The equation is now solved.

$$x=2\sqrt{53} x=-2\sqrt{53}$$