Solve for x 4 square root of x = square root of 9x+9

$4 \sqrt{x} = \sqrt{9 x + 9}$

Step 1

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

${(4 \sqrt{x})}^{2} = {\sqrt{9 x + 9}}^{2}$

Step 2

Simplify each side of the equation.

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

${(4 x^{\frac{1}{2}})}^{2} = {\sqrt{9 x + 9}}^{2}$

Simplify the left side.

Simplify ${(4 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $4 x^{\frac{1}{2}}$ .

$4^{2} {(x^{\frac{1}{2}})}^{2} = {\sqrt{9 x + 9}}^{2}$

Raise $4$ to the power of $2$ .

$16 {(x^{\frac{1}{2}})}^{2} = {\sqrt{9 x + 9}}^{2}$

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

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

$16 x^{\frac{1}{2} \cdot 2} = {\sqrt{9 x + 9}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 x^{\frac{1}{2} \cdot 2} = {\sqrt{9 x + 9}}^{2}$

Rewrite the expression.

$16 x^{1} = {\sqrt{9 x + 9}}^{2}$

Simplify.

$16 x = {\sqrt{9 x + 9}}^{2}$

Simplify the right side.

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

Factor $9$ out of $9 x + 9$ .

Factor $9$ out of $9 x$ .

$16 x = {\sqrt{9 (x) + 9}}^{2}$

Factor $9$ out of $9$ .

$16 x = {\sqrt{9 (x) + 9 (1)}}^{2}$

Factor $9$ out of $9 (x) + 9 (1)$ .

$16 x = {\sqrt{9 (x + 1)}}^{2}$

Rewrite $9 (x + 1)$ as $3^{2} (x + 1^{2})$ .

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

$16 x = {\sqrt{3^{2} (x + 1)}}^{2}$

Rewrite $1$ as $1^{2}$ .

$16 x = {\sqrt{3^{2} (x + 1^{2})}}^{2}$

Pull terms out from under the radical.

$16 x = {(3 \sqrt{x + 1^{2}})}^{2}$

Simplify the expression.

One to any power is one.

$16 x = {(3 \sqrt{x + 1})}^{2}$

Apply the product rule to $3 \sqrt{x + 1}$ .

$16 x = 3^{2} {\sqrt{x + 1}}^{2}$

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

$16 x = 9 {\sqrt{x + 1}}^{2}$

Rewrite ${\sqrt{x + 1}}^{2}$ as $x + 1$ .

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

$16 x = 9 {({(x + 1)}^{\frac{1}{2}})}^{2}$

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

$16 x = 9 {(x + 1)}^{\frac{1}{2} \cdot 2}$

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

$16 x = 9 {(x + 1)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 x = 9 {(x + 1)}^{\frac{2}{2}}$

Rewrite the expression.

$16 x = 9 {(x + 1)}^{1}$

Simplify.

$16 x = 9 (x + 1)$

Apply the distributive property.

$16 x = 9 x + 9 \cdot 1$

Multiply $9$ by $1$ .

$16 x = 9 x + 9$

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.

$16 x - 9 x = 9$

Subtract $9 x$ from $16 x$ .

$7 x = 9$

Divide each term in $7 x = 9$ by $7$ and simplify.

Divide each term in $7 x = 9$ by $7$ .

$\frac{7 x}{7} = \frac{9}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{9}{7}$

Divide $x$ by $1$ .

$x = \frac{9}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{7}$

Decimal Form:

$x = 1.\overline{285714}$

Mixed Number Form:

$x = 1 \frac{2}{7}$

Solve for x 4 square root of x = square root of 9x+9

Related Questions

Support LCMGCF.com by disabling your adblocker.