Finite Math Examples

$4 {(x + 1)}^{2} - 80 = 0$

Step 1

Simplify $4 {(x + 1)}^{2} - 80$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$4 ((x + 1) (x + 1)) - 80 = 0$

Step 1.1.2

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

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Step 1.1.2.1

Apply the distributive property.

$4 (x (x + 1) + 1 (x + 1)) - 80 = 0$

Step 1.1.2.2

Apply the distributive property.

$4 (x \cdot x + x \cdot 1 + 1 (x + 1)) - 80 = 0$

Step 1.1.2.3

Apply the distributive property.

$4 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) - 80 = 0$

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 $x$ by $x$ .

$4 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) - 80 = 0$

Step 1.1.3.1.2

Multiply $x$ by $1$ .

$4 (x^{2} + x + 1 x + 1 \cdot 1) - 80 = 0$

Step 1.1.3.1.3

Multiply $x$ by $1$ .

$4 (x^{2} + x + x + 1 \cdot 1) - 80 = 0$

Step 1.1.3.1.4

Multiply $1$ by $1$ .

$4 (x^{2} + x + x + 1) - 80 = 0$

Step 1.1.3.2

Add $x$ and $x$ .

$4 (x^{2} + 2 x + 1) - 80 = 0$

Step 1.1.4

Apply the distributive property.

$4 x^{2} + 4 (2 x) + 4 \cdot 1 - 80 = 0$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Multiply $2$ by $4$ .

$4 x^{2} + 8 x + 4 \cdot 1 - 80 = 0$

Step 1.1.5.2

Multiply $4$ by $1$ .

$4 x^{2} + 8 x + 4 - 80 = 0$

Step 1.2

Subtract $80$ from $4$ .

$4 x^{2} + 8 x - 76 = 0$

Step 2

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

$x = - 1 - 2 \sqrt{5}, - 1 + 2 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - 1 - 2 \sqrt{5}, - 1 + 2 \sqrt{5}$

Decimal Form:

$x = - 5.47213595 \dots, 3.47213595 \dots$

Step 4