Solve for c 10b=5( square root of c+2)

$10 b = 5 (\sqrt{c} + 2)$

Rewrite the equation as $5 (\sqrt{c} + 2) = 10 b$ .

$5 (\sqrt{c} + 2) = 10 b$

Divide each term in $5 (\sqrt{c} + 2) = 10 b$ by $5$ and simplify.

Divide each term in $5 (\sqrt{c} + 2) = 10 b$ by $5$ .

$\frac{5 (\sqrt{c} + 2)}{5} = \frac{10 b}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (\sqrt{c} + 2)}{5} = \frac{10 b}{5}$

Divide $\sqrt{c} + 2$ by $1$ .

$\sqrt{c} + 2 = \frac{10 b}{5}$

Simplify the right side.

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 b$ .

$\sqrt{c} + 2 = \frac{5 (2 b)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$\sqrt{c} + 2 = \frac{5 (2 b)}{5 (1)}$

Cancel the common factor.

$\sqrt{c} + 2 = \frac{5 (2 b)}{5 \cdot 1}$

Rewrite the expression.

$\sqrt{c} + 2 = \frac{2 b}{1}$

Divide $2 b$ by $1$ .

$\sqrt{c} + 2 = 2 b$

Subtract $2$ from both sides of the equation.

$\sqrt{c} = 2 b - 2$

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

${\sqrt{c}}^{2} = {(2 b - 2)}^{2}$

Simplify each side of the equation.

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

${(c^{\frac{1}{2}})}^{2} = {(2 b - 2)}^{2}$

Simplify the left side.

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

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

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

$c^{\frac{1}{2} \cdot 2} = {(2 b - 2)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$c^{\frac{1}{2} \cdot 2} = {(2 b - 2)}^{2}$

Rewrite the expression.

$c^{1} = {(2 b - 2)}^{2}$

Simplify.

$c = {(2 b - 2)}^{2}$

Simplify the right side.

Simplify ${(2 b - 2)}^{2}$ .

Rewrite ${(2 b - 2)}^{2}$ as $(2 b - 2) (2 b - 2)$ .

$c = (2 b - 2) (2 b - 2)$

Expand $(2 b - 2) (2 b - 2)$ using the FOIL Method.

Apply the distributive property.

$c = 2 b (2 b - 2) - 2 (2 b - 2)$

Apply the distributive property.

$c = 2 b (2 b) + 2 b \cdot - 2 - 2 (2 b - 2)$

Apply the distributive property.

$c = 2 b (2 b) + 2 b \cdot - 2 - 2 (2 b) - 2 \cdot - 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$c = 2 \cdot 2 b \cdot b + 2 b \cdot - 2 - 2 (2 b) - 2 \cdot - 2$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$c = 2 \cdot 2 (b \cdot b) + 2 b \cdot - 2 - 2 (2 b) - 2 \cdot - 2$

Multiply $b$ by $b$ .

$c = 2 \cdot 2 b^{2} + 2 b \cdot - 2 - 2 (2 b) - 2 \cdot - 2$

Multiply $2$ by $2$ .

$c = 4 b^{2} + 2 b \cdot - 2 - 2 (2 b) - 2 \cdot - 2$

Multiply $- 2$ by $2$ .

$c = 4 b^{2} - 4 b - 2 (2 b) - 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$c = 4 b^{2} - 4 b - 4 b - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$c = 4 b^{2} - 4 b - 4 b + 4$

Subtract $4 b$ from $- 4 b$ .

$c = 4 b^{2} - 8 b + 4$

Solve for c 10b=5( square root of c+2)

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