Finite Math Examples

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

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

Step 1

Set

- 2 {(x + 1)}^{2} - 2

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

0

$0$ .

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

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

Step 2

Solve for

x

$x$ .

Tap for more steps...

Step 2.1

Simplify

- 2 {(x + 1)}^{2} - 2

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

Tap for more steps...

Step 2.1.1

Simplify each term.

Tap for more steps...

Step 2.1.1.1

Rewrite

{(x + 1)}^{2}

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

(x + 1) (x + 1)

$(x + 1) (x + 1)$ .

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

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

Step 2.1.1.2

Expand

(x + 1) (x + 1)

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

Tap for more steps...

Step 2.1.1.2.1

Apply the distributive property.

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

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

Step 2.1.1.2.2

Apply the distributive property.

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

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

Step 2.1.1.2.3

Apply the distributive property.

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

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

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

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

Step 2.1.1.3

Simplify and combine like terms.

Tap for more steps...

Step 2.1.1.3.1

Simplify each term.

Tap for more steps...

Step 2.1.1.3.1.1

Multiply

x

$x$ by

x

$x$ .

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

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

Step 2.1.1.3.1.2

Multiply

x

$x$ by

1

$1$ .

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

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

Step 2.1.1.3.1.3

Multiply

x

$x$ by

1

$1$ .

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

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

Step 2.1.1.3.1.4

Multiply

1

$1$ by

1

$1$ .

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

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

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

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

Step 2.1.1.3.2

Add

x

$x$ and

x

$x$ .

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

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

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

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

Step 2.1.1.4

Apply the distributive property.

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

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

Step 2.1.1.5

Simplify.

Tap for more steps...

Step 2.1.1.5.1

Multiply

2

$2$ by

- 2

$- 2$ .

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

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

Step 2.1.1.5.2

Multiply

- 2

$- 2$ by

1

$1$ .

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

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

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

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

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

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

Step 2.1.2

Subtract

2

$2$ from

- 2

$- 2$ .

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

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

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

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

Step 2.2

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

No solution