Solve x^2+x^2=2222222

$${ x }^{ 2 } + { x }^{ 2 } =2222222$$

Solve for x

$$x=\sqrt{1111111}\approx 1054.092500685$$

$$x=-\sqrt{1111111}\approx -1054.092500685$$

Steps by Finding Square Root

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

$$2x^{2}=2222222$$

Divide both sides by 2.

$$x^{2}=\frac{2222222}{2}$$

Divide 2222222 by 2 to get 1111111.

$$x^{2}=1111111$$

Take the square root of both sides of the equation.

$$x=\sqrt{1111111} x=-\sqrt{1111111}$$

Steps Using the Quadratic Formula

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

$$2x^{2}=2222222$$

Subtract 2222222 from both sides.

$$2x^{2}-2222222=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -2222222 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-2222222\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-2222222\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-2222222\right)}}{2\times 2}$$

Multiply -8 times -2222222.

$$x=\frac{0±\sqrt{17777776}}{2\times 2}$$

Take the square root of 17777776.

$$x=\frac{0±4\sqrt{1111111}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{1111111}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{1111111}}{4} when ± is plus.

$$x=\sqrt{1111111}$$

Now solve the equation x=\frac{0±4\sqrt{1111111}}{4} when ± is minus.

$$x=-\sqrt{1111111}$$

The equation is now solved.

$$x=\sqrt{1111111} x=-\sqrt{1111111}$$