Finite Math Examples

$4 {| x + 1 |}^{3} + 5 {(x + 1)}^{2} - | x + 1 | = 2$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$4 {| x + 1 |}^{3} + 5 ((x + 1) (x + 1)) - | x + 1 | = 2$

Step 1.2

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

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$4 {| x + 1 |}^{3} + 5 (x (x + 1) + 1 (x + 1)) - | x + 1 | = 2$

Step 1.2.2

Apply the distributive property.

$4 {| x + 1 |}^{3} + 5 (x \cdot x + x \cdot 1 + 1 (x + 1)) - | x + 1 | = 2$

Step 1.2.3

Apply the distributive property.

$4 {| x + 1 |}^{3} + 5 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) - | x + 1 | = 2$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $x$ by $x$ .

$4 {| x + 1 |}^{3} + 5 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) - | x + 1 | = 2$

Step 1.3.1.2

Multiply $x$ by $1$ .

$4 {| x + 1 |}^{3} + 5 (x^{2} + x + 1 x + 1 \cdot 1) - | x + 1 | = 2$

Step 1.3.1.3

Multiply $x$ by $1$ .

$4 {| x + 1 |}^{3} + 5 (x^{2} + x + x + 1 \cdot 1) - | x + 1 | = 2$

Step 1.3.1.4

Multiply $1$ by $1$ .

$4 {| x + 1 |}^{3} + 5 (x^{2} + x + x + 1) - | x + 1 | = 2$

Step 1.3.2

Add $x$ and $x$ .

$4 {| x + 1 |}^{3} + 5 (x^{2} + 2 x + 1) - | x + 1 | = 2$

Step 1.4

Apply the distributive property.

$4 {| x + 1 |}^{3} + 5 x^{2} + 5 (2 x) + 5 \cdot 1 - | x + 1 | = 2$

Step 1.5

Simplify.

Tap for more steps...

Step 1.5.1

Multiply $2$ by $5$ .

$4 {| x + 1 |}^{3} + 5 x^{2} + 10 x + 5 \cdot 1 - | x + 1 | = 2$

Step 1.5.2

Multiply $5$ by $1$ .

$4 {| x + 1 |}^{3} + 5 x^{2} + 10 x + 5 - | x + 1 | = 2$

Step 2

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

$x \approx - 1.59307033, - 0.40692966$

Step 3