Solve for x 3x^2-6=10-x^2

$3 x^{2} - 6 = 10 - x^{2}$

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

Add $x^{2}$ to both sides of the equation.

$3 x^{2} - 6 + x^{2} = 10$

Add $3 x^{2}$ and $x^{2}$ .

$4 x^{2} - 6 = 10$

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

Add $6$ to both sides of the equation.

$4 x^{2} = 10 + 6$

Add $10$ and $6$ .

$4 x^{2} = 16$

Divide each term in $4 x^{2} = 16$ by $4$ and simplify.

Divide each term in $4 x^{2} = 16$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{16}{4}$

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

$x^{2} = \frac{16}{4}$

Simplify the right side.

Divide $16$ by $4$ .

$x^{2} = 4$

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

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

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

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

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$