Solve for l S=2 square root of l-9

$S = 2 \sqrt{l} - 9$

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

$2 \sqrt{l} - 9 = S$

Add $9$ to both sides of the equation.

$2 \sqrt{l} = S + 9$

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

${(2 \sqrt{l})}^{2} = {(S + 9)}^{2}$

Simplify each side of the equation.

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

${(2 l^{\frac{1}{2}})}^{2} = {(S + 9)}^{2}$

Simplify the left side.

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

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

$2^{2} {(l^{\frac{1}{2}})}^{2} = {(S + 9)}^{2}$

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

$4 {(l^{\frac{1}{2}})}^{2} = {(S + 9)}^{2}$

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

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

$4 l^{\frac{1}{2} \cdot 2} = {(S + 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 l^{\frac{1}{2} \cdot 2} = {(S + 9)}^{2}$

Rewrite the expression.

$4 l^{1} = {(S + 9)}^{2}$

Simplify.

$4 l = {(S + 9)}^{2}$

Simplify the right side.

Simplify ${(S + 9)}^{2}$ .

Rewrite ${(S + 9)}^{2}$ as $(S + 9) (S + 9)$ .

$4 l = (S + 9) (S + 9)$

Expand $(S + 9) (S + 9)$ using the FOIL Method.

Apply the distributive property.

$4 l = S (S + 9) + 9 (S + 9)$

Apply the distributive property.

$4 l = S \cdot S + S \cdot 9 + 9 (S + 9)$

Apply the distributive property.

$4 l = S \cdot S + S \cdot 9 + 9 S + 9 \cdot 9$

Simplify and combine like terms.

Simplify each term.

Multiply $S$ by $S$ .

$4 l = S^{2} + S \cdot 9 + 9 S + 9 \cdot 9$

Move $9$ to the left of $S$ .

$4 l = S^{2} + 9 \cdot S + 9 S + 9 \cdot 9$

Multiply $9$ by $9$ .

$4 l = S^{2} + 9 S + 9 S + 81$

Add $9 S$ and $9 S$ .

$4 l = S^{2} + 18 S + 81$

Divide each term in $4 l = S^{2} + 18 S + 81$ by $4$ and simplify.

Divide each term in $4 l = S^{2} + 18 S + 81$ by $4$ .

$\frac{4 l}{4} = \frac{S^{2}}{4} + \frac{18 S}{4} + \frac{81}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 l}{4} = \frac{S^{2}}{4} + \frac{18 S}{4} + \frac{81}{4}$

Divide $l$ by $1$ .

$l = \frac{S^{2}}{4} + \frac{18 S}{4} + \frac{81}{4}$

Simplify the right side.

Cancel the common factor of $18$ and $4$ .

Factor $2$ out of $18 S$ .

$l = \frac{S^{2}}{4} + \frac{2 (9 S)}{4} + \frac{81}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$l = \frac{S^{2}}{4} + \frac{2 (9 S)}{2 (2)} + \frac{81}{4}$

Cancel the common factor.

$l = \frac{S^{2}}{4} + \frac{2 (9 S)}{2 \cdot 2} + \frac{81}{4}$

Rewrite the expression.

$l = \frac{S^{2}}{4} + \frac{9 S}{2} + \frac{81}{4}$

Solve for l S=2 square root of l-9

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