Solve for x 10x^2-64=36+6x^2

$10 x^{2} - 64 = 36 + 6 x^{2}$

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

Subtract $6 x^{2}$ from both sides of the equation.

$10 x^{2} - 64 - 6 x^{2} = 36$

Subtract $6 x^{2}$ from $10 x^{2}$ .

$4 x^{2} - 64 = 36$

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

Add $64$ to both sides of the equation.

$4 x^{2} = 36 + 64$

Add $36$ and $64$ .

$4 x^{2} = 100$

Divide each term in $4 x^{2} = 100$ by $4$ and simplify.

Divide each term in $4 x^{2} = 100$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{100}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{100}{4}$

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

$x^{2} = \frac{100}{4}$

Simplify the right side.

Divide $100$ by $4$ .

$x^{2} = 25$

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

$x = \pm \sqrt{25}$

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.

$x = \pm 5$

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.

$x = 5, - 5$