Solve for x (10-6x)^(1/2)=(3x+4)^(1/2)

${(10 - 6 x)}^{\frac{1}{2}} = {(3 x + 4)}^{\frac{1}{2}}$

Step 1

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$10 - 6 x = 3 x + 4$

Step 2

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$10 - 6 x - 3 x = 4$

Subtract $3 x$ from $- 6 x$ .

$10 - 9 x = 4$

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

Subtract $10$ from both sides of the equation.

$- 9 x = 4 - 10$

Subtract $10$ from $4$ .

$- 9 x = - 6$

Divide each term in $- 9 x = - 6$ by $- 9$ and simplify.

Divide each term in $- 9 x = - 6$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 6}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 6}{- 9}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 9}$

Simplify the right side.

Cancel the common factor of $- 6$ and $- 9$ .

Factor $- 3$ out of $- 6$ .

$x = \frac{- 3 (2)}{- 9}$

Cancel the common factors.

Factor $- 3$ out of $- 9$ .

$x = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Cancel the common factor.

$x = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Rewrite the expression.

$x = \frac{2}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$