Solve for I 9=2 square root of I-9

$9 = 2 \sqrt{I} - 9$

Step 1

Rewrite the equation as $2 \sqrt{I} - 9 = 9$ .

$2 \sqrt{I} - 9 = 9$

Step 2

Move all terms not containing $2 \sqrt{I}$ to the right side of the equation.

Add $9$ to both sides of the equation.

$2 \sqrt{I} = 9 + 9$

Add $9$ and $9$ .

$2 \sqrt{I} = 18$

Step 3

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

${(2 \sqrt{I})}^{2} = 18^{2}$

Step 4

Simplify each side of the equation.

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

${(2 I^{\frac{1}{2}})}^{2} = 18^{2}$

Simplify the left side.

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

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

$2^{2} {(I^{\frac{1}{2}})}^{2} = 18^{2}$

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

$4 {(I^{\frac{1}{2}})}^{2} = 18^{2}$

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

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

$4 I^{\frac{1}{2} \cdot 2} = 18^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 I^{\frac{1}{2} \cdot 2} = 18^{2}$

Rewrite the expression.

$4 I^{1} = 18^{2}$

Simplify.

$4 I = 18^{2}$

Simplify the right side.

Raise $18$ to the power of $2$ .

$4 I = 324$

Step 5

Divide each term in $4 I = 324$ by $4$ and simplify.

Divide each term in $4 I = 324$ by $4$ .

$\frac{4 I}{4} = \frac{324}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 I}{4} = \frac{324}{4}$

Divide $I$ by $1$ .

$I = \frac{324}{4}$

Simplify the right side.

Divide $324$ by $4$ .

$I = 81$

Solve for I 9=2 square root of I-9

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