Solve x^2+x^2-13=130

$${ x }^{ 2 } + { x }^{ 2 } -13=130$$

Solve for x

$$x = \frac{\sqrt{286}}{2} \approx 8.455767263$$

$$x = -\frac{\sqrt{286}}{2} \approx -8.455767263$$

Steps by Finding Square Root

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-13=130$$

Add 13 to both sides.

$$2x^{2}=130+13$$

Add 130 and 13 to get 143.

$$2x^{2}=143$$

Divide both sides by 2.

$$x^{2}=\frac{143}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{286}}{2} x=-\frac{\sqrt{286}}{2}$$

Steps Using the Quadratic Formula

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-13=130$$

Subtract 130 from both sides.

$$2x^{2}-13-130=0$$

Subtract 130 from -13 to get -143.

$$2x^{2}-143=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -143 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-143\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-143\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-143\right)}}{2\times 2}$$

Multiply -8 times -143.

$$x=\frac{0±\sqrt{1144}}{2\times 2}$$

Take the square root of 1144.

$$x=\frac{0±2\sqrt{286}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{286}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{286}}{4} when ± is plus.

$$x=\frac{\sqrt{286}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{286}}{4} when ± is minus.

$$x=-\frac{\sqrt{286}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{286}}{2} x=-\frac{\sqrt{286}}{2}$$