Basic Math Examples

$c + 2 = \sqrt{15 c + 4}$

Step 1

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\sqrt{15 c + 4} = c + 2$

Step 2

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

${\sqrt{15 c + 4}}^{2} = {(c + 2)}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15 c + 4}$ as ${(15 c + 4)}^{\frac{1}{2}}$ .

${({(15 c + 4)}^{\frac{1}{2}})}^{2} = {(c + 2)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(15 c + 4)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(15 c + 4)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(15 c + 4)}^{\frac{1}{2} \cdot 2} = {(c + 2)}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(15 c + 4)}^{\frac{1}{2} \cdot 2} = {(c + 2)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(15 c + 4)}^{1} = {(c + 2)}^{2}$

Step 3.2.1.2

Simplify.

$15 c + 4 = {(c + 2)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(c + 2)}^{2}$ .

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Step 3.3.1.1

Rewrite ${(c + 2)}^{2}$ as $(c + 2) (c + 2)$ .

$15 c + 4 = (c + 2) (c + 2)$

Step 3.3.1.2

Expand $(c + 2) (c + 2)$ using the FOIL Method.

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Step 3.3.1.2.1

Apply the distributive property.

$15 c + 4 = c (c + 2) + 2 (c + 2)$

Step 3.3.1.2.2

Apply the distributive property.

$15 c + 4 = c \cdot c + c \cdot 2 + 2 (c + 2)$

Step 3.3.1.2.3

Apply the distributive property.

$15 c + 4 = c \cdot c + c \cdot 2 + 2 c + 2 \cdot 2$

Step 3.3.1.3

Simplify and combine like terms.

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Step 3.3.1.3.1

Simplify each term.

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Step 3.3.1.3.1.1

Multiply $c$ by $c$ .

$15 c + 4 = c^{2} + c \cdot 2 + 2 c + 2 \cdot 2$

Step 3.3.1.3.1.2

Move $2$ to the left of $c$ .

$15 c + 4 = c^{2} + 2 \cdot c + 2 c + 2 \cdot 2$

Step 3.3.1.3.1.3

Multiply $2$ by $2$ .

$15 c + 4 = c^{2} + 2 c + 2 c + 4$

Step 3.3.1.3.2

Add $2 c$ and $2 c$ .

$15 c + 4 = c^{2} + 4 c + 4$

Step 4

Solve for $c$ .

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Step 4.1

Since $c$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$c^{2} + 4 c + 4 = 15 c + 4$

Step 4.2

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

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Step 4.2.1

Subtract $15 c$ from both sides of the equation.

$c^{2} + 4 c + 4 - 15 c = 4$

Step 4.2.2

Subtract $15 c$ from $4 c$ .

$c^{2} - 11 c + 4 = 4$

Step 4.3

Subtract $4$ from both sides of the equation.

$c^{2} - 11 c + 4 - 4 = 0$

Step 4.4

Combine the opposite terms in $c^{2} - 11 c + 4 - 4$ .

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Step 4.4.1

Subtract $4$ from $4$ .

$c^{2} - 11 c + 0 = 0$

Step 4.4.2

Add $c^{2} - 11 c$ and $0$ .

$c^{2} - 11 c = 0$

Step 4.5

Factor $c$ out of $c^{2} - 11 c$ .

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Step 4.5.1

Factor $c$ out of $c^{2}$ .

$c \cdot c - 11 c = 0$

Step 4.5.2

Factor $c$ out of $- 11 c$ .

$c \cdot c + c \cdot - 11 = 0$

Step 4.5.3

Factor $c$ out of $c \cdot c + c \cdot - 11$ .

$c (c - 11) = 0$

Step 4.6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$c = 0$

$c - 11 = 0$

Step 4.7

Set $c$ equal to $0$ .

$c = 0$

Step 4.8

Set $c - 11$ equal to $0$ and solve for $c$ .

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Step 4.8.1

Set $c - 11$ equal to $0$ .

$c - 11 = 0$

Step 4.8.2

Add $11$ to both sides of the equation.

$c = 11$

Step 4.9

The final solution is all the values that make $c (c - 11) = 0$ true.

$c = 0, 11$