Finite Math Examples

$f (x) = - 2 {(x + 1)}^{2} - 2$

Step 1

Set $- 2 {(x + 1)}^{2} - 2$ equal to $0$ .

$- 2 {(x + 1)}^{2} - 2 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify $- 2 {(x + 1)}^{2} - 2$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$- 2 ((x + 1) (x + 1)) - 2 = 0$

Step 2.1.1.2

Expand $(x + 1) (x + 1)$ using the FOIL Method.

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Step 2.1.1.2.1

Apply the distributive property.

$- 2 (x (x + 1) + 1 (x + 1)) - 2 = 0$

Step 2.1.1.2.2

Apply the distributive property.

$- 2 (x \cdot x + x \cdot 1 + 1 (x + 1)) - 2 = 0$

Step 2.1.1.2.3

Apply the distributive property.

$- 2 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) - 2 = 0$

Step 2.1.1.3

Simplify and combine like terms.

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Step 2.1.1.3.1

Simplify each term.

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Step 2.1.1.3.1.1

Multiply $x$ by $x$ .

$- 2 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) - 2 = 0$

Step 2.1.1.3.1.2

Multiply $x$ by $1$ .

$- 2 (x^{2} + x + 1 x + 1 \cdot 1) - 2 = 0$

Step 2.1.1.3.1.3

Multiply $x$ by $1$ .

$- 2 (x^{2} + x + x + 1 \cdot 1) - 2 = 0$

Step 2.1.1.3.1.4

Multiply $1$ by $1$ .

$- 2 (x^{2} + x + x + 1) - 2 = 0$

Step 2.1.1.3.2

Add $x$ and $x$ .

$- 2 (x^{2} + 2 x + 1) - 2 = 0$

Step 2.1.1.4

Apply the distributive property.

$- 2 x^{2} - 2 (2 x) - 2 \cdot 1 - 2 = 0$

Step 2.1.1.5

Simplify.

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Step 2.1.1.5.1

Multiply $2$ by $- 2$ .

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

Step 2.1.1.5.2

Multiply $- 2$ by $1$ .

$- 2 x^{2} - 4 x - 2 - 2 = 0$

Step 2.1.2

Subtract $2$ from $- 2$ .

$- 2 x^{2} - 4 x - 4 = 0$

Step 2.2

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

No solution