Solve x^2=7^2+9^2

$$x ^ { 2 } = 7 ^ { 2 } + 9 ^ { 2 }$$

Solve for x

$$x=\sqrt{130}\approx 11.401754251$$

$$x=-\sqrt{130}\approx -11.401754251$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$x^{2}=49+9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}=49+81$$

Add 49 and 81 to get 130.

$$x^{2}=130$$

Take the square root of both sides of the equation.

$$x=\sqrt{130} x=-\sqrt{130}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$x^{2}=49+9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}=49+81$$

Add 49 and 81 to get 130.

$$x^{2}=130$$

Subtract 130 from both sides.

$$x^{2}-130=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -130 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-130\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-130\right)}}{2}$$

Multiply -4 times -130.

$$x=\frac{0±\sqrt{520}}{2}$$

Take the square root of 520.

$$x=\frac{0±2\sqrt{130}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{130}}{2} when ± is plus.

$$x=\sqrt{130}$$

Now solve the equation x=\frac{0±2\sqrt{130}}{2} when ± is minus.

$$x=-\sqrt{130}$$

The equation is now solved.

$$x=\sqrt{130} x=-\sqrt{130}$$