Solve for x 8 square root of x-10=6 square root of x

$8 \sqrt{x} - 10 = 6 \sqrt{x}$

Solve for $\sqrt{x}$ .

Move all terms containing $\sqrt{x}$ to the left side of the equation.

Subtract $6 \sqrt{x}$ from both sides of the equation.

$8 \sqrt{x} - 10 - 6 \sqrt{x} = 0$

Subtract $6 \sqrt{x}$ from $8 \sqrt{x}$ .

$2 \sqrt{x} - 10 = 0$

Add $10$ to both sides of the equation.

$2 \sqrt{x} = 10$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $\sqrt{x}$ by $1$ .

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

Simplify the right side.

Divide $10$ by $2$ .

$\sqrt{x} = 5$

To remove the radical on the left side of the equation, square both sides of the equation.

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

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

$x^{1} = 5^{2}$

Simplify.

$x = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$x = 25$