Solve for x square root of 7x+5 = square root of 9x

$\sqrt{7 x + 5} = \sqrt{9 x}$

Step 1

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

${\sqrt{7 x + 5}}^{2} = {\sqrt{9 x}}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x + 5}$ as ${(7 x + 5)}^{\frac{1}{2}}$ .

${({(7 x + 5)}^{\frac{1}{2}})}^{2} = {\sqrt{9 x}}^{2}$

Simplify the left side.

Simplify ${({(7 x + 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(7 x + 5)}^{\frac{1}{2}})}^{2}$ .

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

${(7 x + 5)}^{\frac{1}{2} \cdot 2} = {\sqrt{9 x}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 x + 5)}^{\frac{1}{2} \cdot 2} = {\sqrt{9 x}}^{2}$

Rewrite the expression.

${(7 x + 5)}^{1} = {\sqrt{9 x}}^{2}$

Simplify.

$7 x + 5 = {\sqrt{9 x}}^{2}$

Simplify the right side.

Simplify ${\sqrt{9 x}}^{2}$ .

Rewrite $9$ as $3^{2}$ .

$7 x + 5 = {\sqrt{3^{2} x}}^{2}$

Pull terms out from under the radical.

$7 x + 5 = {(3 \sqrt{x})}^{2}$

Simplify the expression.

Apply the product rule to $3 \sqrt{x}$ .

$7 x + 5 = 3^{2} {\sqrt{x}}^{2}$

Raise $3$ to the power of $2$ .

$7 x + 5 = 9 {\sqrt{x}}^{2}$

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

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

$7 x + 5 = 9 {(x^{\frac{1}{2}})}^{2}$

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

$7 x + 5 = 9 x^{\frac{1}{2} \cdot 2}$

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

$7 x + 5 = 9 x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$7 x + 5 = 9 x^{\frac{2}{2}}$

Rewrite the expression.

$7 x + 5 = 9 x^{1}$

Simplify.

$7 x + 5 = 9 x$

Step 3

Solve for $x$ .

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

Subtract $9 x$ from both sides of the equation.

$7 x + 5 - 9 x = 0$

Subtract $9 x$ from $7 x$ .

$- 2 x + 5 = 0$

Subtract $5$ from both sides of the equation.

$- 2 x = - 5$

Divide each term in $- 2 x = - 5$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 5$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 5}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 5}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

$x = 2 \frac{1}{2}$

Solve for x square root of 7x+5 = square root of 9x

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