Basic Math Examples

$9 - {(c + 2)}^{2} = 0$

Step 1

Simplify $9 - {(c + 2)}^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$9 - ((c + 2) (c + 2)) = 0$

Step 1.1.2

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

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Step 1.1.2.1

Apply the distributive property.

$9 - (c (c + 2) + 2 (c + 2)) = 0$

Step 1.1.2.2

Apply the distributive property.

$9 - (c \cdot c + c \cdot 2 + 2 (c + 2)) = 0$

Step 1.1.2.3

Apply the distributive property.

$9 - (c \cdot c + c \cdot 2 + 2 c + 2 \cdot 2) = 0$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $c$ by $c$ .

$9 - (c^{2} + c \cdot 2 + 2 c + 2 \cdot 2) = 0$

Step 1.1.3.1.2

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

$9 - (c^{2} + 2 \cdot c + 2 c + 2 \cdot 2) = 0$

Step 1.1.3.1.3

Multiply $2$ by $2$ .

$9 - (c^{2} + 2 c + 2 c + 4) = 0$

Step 1.1.3.2

Add $2 c$ and $2 c$ .

$9 - (c^{2} + 4 c + 4) = 0$

Step 1.1.4

Apply the distributive property.

$9 - c^{2} - (4 c) - 1 \cdot 4 = 0$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Multiply $4$ by $- 1$ .

$9 - c^{2} - 4 c - 1 \cdot 4 = 0$

Step 1.1.5.2

Multiply $- 1$ by $4$ .

$9 - c^{2} - 4 c - 4 = 0$

Step 1.2

Subtract $4$ from $9$ .

$- c^{2} - 4 c + 5 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$c = - 5, 1$

Step 3