Solve for x 2 square root of 10+3x = square root of 7+x

$2 \sqrt{10 + 3 x} = \sqrt{7 + x}$

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

${(2 \sqrt{10 + 3 x})}^{2} = {\sqrt{7 + x}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 + 3 x}$ as ${(10 + 3 x)}^{\frac{1}{2}}$ .

${(2 {(10 + 3 x)}^{\frac{1}{2}})}^{2} = {\sqrt{7 + x}}^{2}$

Simplify the left side.

Simplify ${(2 {(10 + 3 x)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $2 {(10 + 3 x)}^{\frac{1}{2}}$ .

$2^{2} {({(10 + 3 x)}^{\frac{1}{2}})}^{2} = {\sqrt{7 + x}}^{2}$

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

$4 {({(10 + 3 x)}^{\frac{1}{2}})}^{2} = {\sqrt{7 + x}}^{2}$

Multiply the exponents in ${({(10 + 3 x)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(10 + 3 x)}^{\frac{1}{2} \cdot 2} = {\sqrt{7 + x}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(10 + 3 x)}^{\frac{1}{2} \cdot 2} = {\sqrt{7 + x}}^{2}$

Rewrite the expression.

$4 {(10 + 3 x)}^{1} = {\sqrt{7 + x}}^{2}$

Simplify.

$4 (10 + 3 x) = {\sqrt{7 + x}}^{2}$

Apply the distributive property.

$4 \cdot 10 + 4 (3 x) = {\sqrt{7 + x}}^{2}$

Multiply.

Multiply $4$ by $10$ .

$40 + 4 (3 x) = {\sqrt{7 + x}}^{2}$

Multiply $3$ by $4$ .

$40 + 12 x = {\sqrt{7 + x}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{7 + x}}^{2}$ as $7 + x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 + x}$ as ${(7 + x)}^{\frac{1}{2}}$ .

$40 + 12 x = {({(7 + x)}^{\frac{1}{2}})}^{2}$

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

$40 + 12 x = {(7 + x)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$40 + 12 x = {(7 + x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$40 + 12 x = {(7 + x)}^{\frac{2}{2}}$

Rewrite the expression.

$40 + 12 x = {(7 + x)}^{1}$

Simplify.

$40 + 12 x = 7 + x$

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$40 + 12 x - x = 7$

Subtract $x$ from $12 x$ .

$40 + 11 x = 7$

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

Subtract $40$ from both sides of the equation.

$11 x = 7 - 40$

Subtract $40$ from $7$ .

$11 x = - 33$

Divide each term in $11 x = - 33$ by $11$ and simplify.

Divide each term in $11 x = - 33$ by $11$ .

$\frac{11 x}{11} = \frac{- 33}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{- 33}{11}$

Divide $x$ by $1$ .

$x = \frac{- 33}{11}$

Simplify the right side.

Divide $- 33$ by $11$ .

$x = - 3$

Solve for x 2 square root of 10+3x = square root of 7+x

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