Solve for x 2x^2+5=x^2+30

$2 x^{2} + 5 = x^{2} + 30$

Step 1

Move all terms containing $x$ to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$2 x^{2} + 5 - x^{2} = 30$

Subtract $x^{2}$ from $2 x^{2}$ .

$x^{2} + 5 = 30$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$x^{2} = 30 - 5$

Subtract $5$ from $30$ .

$x^{2} = 25$

Step 3

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

$x = \pm \sqrt{25}$

Step 4

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 5$

Step 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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$