Solve 23^2=9^2+x^2

$${ 23 }^{ 2 } = { 9 }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x=8\sqrt{7}\approx 21.166010489$$

$$x=-8\sqrt{7}\approx -21.166010489$$

Steps by Finding Square Root

Calculate 23 to the power of 2 and get 529.

$$529=9^{2}+x^{2}$$

Calculate 9 to the power of 2 and get 81.

$$529=81+x^{2}$$

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

$$81+x^{2}=529$$

Subtract 81 from both sides.

$$x^{2}=529-81$$

Subtract 81 from 529 to get 448.

$$x^{2}=448$$

Take the square root of both sides of the equation.

$$x=8\sqrt{7} x=-8\sqrt{7}$$

Steps Using the Quadratic Formula

Calculate 23 to the power of 2 and get 529.

$$529=9^{2}+x^{2}$$

Calculate 9 to the power of 2 and get 81.

$$529=81+x^{2}$$

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

$$81+x^{2}=529$$

Subtract 529 from both sides.

$$81+x^{2}-529=0$$

Subtract 529 from 81 to get -448.

$$-448+x^{2}=0$$

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.

$$x^{2}-448=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -448 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-448\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-448\right)}}{2}$$

Multiply -4 times -448.

$$x=\frac{0±\sqrt{1792}}{2}$$

Take the square root of 1792.

$$x=\frac{0±16\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{7}}{2} when ± is plus.

$$x=8\sqrt{7}$$

Now solve the equation x=\frac{0±16\sqrt{7}}{2} when ± is minus.

$$x=-8\sqrt{7}$$

The equation is now solved.

$$x=8\sqrt{7} x=-8\sqrt{7}$$