Solve for x square root of 3x+2- square root of 2x+7=0

$\sqrt{3 x + 2} - \sqrt{2 x + 7} = 0$

Step 1

Add $\sqrt{2 x + 7}$ to both sides of the equation.

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

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 x + 2 = {(2 x + 7)}^{1}$

Simplify.

$3 x + 2 = 2 x + 7$

Step 4

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$3 x + 2 - 2 x = 7$

Subtract $2 x$ from $3 x$ .

$x + 2 = 7$

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

Subtract $2$ from both sides of the equation.

$x = 7 - 2$

Subtract $2$ from $7$ .

$x = 5$

Solve for x square root of 3x+2- square root of 2x+7=0

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