Solve for z 2z^2=10

$2 z^{2} = 10$

Step 1

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $10$ by $2$ .

$z^{2} = 5$

Step 2

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

$z = \pm \sqrt{5}$

Step 3

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.

$z = \sqrt{5}$

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

$z = - \sqrt{5}$

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$z = 2.23606797 \dots, - 2.23606797 \dots$