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

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

Solve for x

$$x=\sqrt{21}\approx 4.582575695$$

$$x=-\sqrt{21}\approx -4.582575695$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

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

Calculate 2 to the power of 2 and get 4.

$$25=4+x^{2}$$

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

$$4+x^{2}=25$$

Subtract 4 from both sides.

$$x^{2}=25-4$$

Subtract 4 from 25 to get 21.

$$x^{2}=21$$

Take the square root of both sides of the equation.

$$x=\sqrt{21} x=-\sqrt{21}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

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

Calculate 2 to the power of 2 and get 4.

$$25=4+x^{2}$$

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

$$4+x^{2}=25$$

Subtract 25 from both sides.

$$4+x^{2}-25=0$$

Subtract 25 from 4 to get -21.

$$-21+x^{2}=0$$

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.

$$x^{2}-21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-21\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-21\right)}}{2}$$

Multiply -4 times -21.

$$x=\frac{0±\sqrt{84}}{2}$$

Take the square root of 84.

$$x=\frac{0±2\sqrt{21}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{2} when ± is plus.

$$x=\sqrt{21}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{2} when ± is minus.

$$x=-\sqrt{21}$$

The equation is now solved.

$$x=\sqrt{21} x=-\sqrt{21}$$