Solve x^2+x^2=1058

$$x ^ { 2 } + x ^ { 2 } = 1058$$

Solve for x

$$x=23$$

$$x=-23$$

Steps Using Difference of Squares

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

$$2x^{2}=1058$$

Subtract 1058 from both sides.

$$2x^{2}-1058=0$$

Divide both sides by 2.

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

Consider x^{2}-529. Rewrite x^{2}-529 as x^{2}-23^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-23\right)\left(x+23\right)=0$$

To find equation solutions, solve x-23=0 and x+23=0.

$$x=23 x=-23$$

Steps by Finding Square Root

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

$$2x^{2}=1058$$

Divide both sides by 2.

$$x^{2}=\frac{1058}{2}$$

Divide 1058 by 2 to get 529.

$$x^{2}=529$$

Take the square root of both sides of the equation.

$$x=23 x=-23$$

Steps Using the Quadratic Formula

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

$$2x^{2}=1058$$

Subtract 1058 from both sides.

$$2x^{2}-1058=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -1058 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-1058\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-1058\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-1058\right)}}{2\times 2}$$

Multiply -8 times -1058.

$$x=\frac{0±\sqrt{8464}}{2\times 2}$$

Take the square root of 8464.

$$x=\frac{0±92}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±92}{4}$$

Now solve the equation x=\frac{0±92}{4} when ± is plus. Divide 92 by 4.

$$x=23$$

Now solve the equation x=\frac{0±92}{4} when ± is minus. Divide -92 by 4.

$$x=-23$$

The equation is now solved.

$$x=23 x=-23$$