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

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

Step 1

Move all terms not containing $\sqrt{3 x}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

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

Subtract $2$ from $7$ .

$\sqrt{3 x} = 5$

Step 2

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

${\sqrt{3 x}}^{2} = 5^{2}$

Step 3

Simplify each side of the equation.

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

${({(3 x)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

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

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

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

${(3 x)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(3 x)}^{1} = 5^{2}$

Simplify.

$3 x = 5^{2}$

Simplify the right side.

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

$3 x = 25$

Step 4

Divide each term in $3 x = 25$ by $3$ and simplify.

Divide each term in $3 x = 25$ by $3$ .

$\frac{3 x}{3} = \frac{25}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{25}{3}$

Divide $x$ by $1$ .

$x = \frac{25}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{3}$

Decimal Form:

$x = 8.\overline{3}$

Mixed Number Form:

$x = 8 \frac{1}{3}$

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

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