Solve x^2+x^2=80

$${ x }^{ 2 } + { x }^{ 2 } = 80$$

Solve for x

$$x=2\sqrt{10}\approx 6.32455532$$

$$x=-2\sqrt{10}\approx -6.32455532$$

Steps by Finding Square Root

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

$$2x^{2}=80$$

Divide both sides by 2.

$$x^{2}=\frac{80}{2}$$

Divide 80 by 2 to get 40.

$$x^{2}=40$$

Take the square root of both sides of the equation.

$$x=2\sqrt{10} x=-2\sqrt{10}$$

Steps Using the Quadratic Formula

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

$$2x^{2}=80$$

Subtract 80 from both sides.

$$2x^{2}-80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-80\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-80\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-80\right)}}{2\times 2}$$

Multiply -8 times -80.

$$x=\frac{0±\sqrt{640}}{2\times 2}$$

Take the square root of 640.

$$x=\frac{0±8\sqrt{10}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8\sqrt{10}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{10}}{4} when ± is plus.

$$x=2\sqrt{10}$$

Now solve the equation x=\frac{0±8\sqrt{10}}{4} when ± is minus.

$$x=-2\sqrt{10}$$

The equation is now solved.

$$x=2\sqrt{10} x=-2\sqrt{10}$$