Find the Roots (Zeros) 2x^2-10=0

$2 x^{2} - 10 = 0$

Add $10$ to both sides of the equation.

$2 x^{2} = 10$

Divide each term in $2 x^{2} = 10$ by $2$ and simplify.

Divide each term in $2 x^{2} = 10$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{10}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x^{2} = 5$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{5}, - \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$