Finite Math Examples

$f (x) = 3 {(x - 8)}^{2} - 27$

Step 1

Set $3 {(x - 8)}^{2} - 27$ equal to $0$ .

$3 {(x - 8)}^{2} - 27 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify $3 {(x - 8)}^{2} - 27$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Rewrite ${(x - 8)}^{2}$ as $(x - 8) (x - 8)$ .

$3 ((x - 8) (x - 8)) - 27 = 0$

Step 2.1.1.2

Expand $(x - 8) (x - 8)$ using the FOIL Method.

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Step 2.1.1.2.1

Apply the distributive property.

$3 (x (x - 8) - 8 (x - 8)) - 27 = 0$

Step 2.1.1.2.2

Apply the distributive property.

$3 (x \cdot x + x \cdot - 8 - 8 (x - 8)) - 27 = 0$

Step 2.1.1.2.3

Apply the distributive property.

$3 (x \cdot x + x \cdot - 8 - 8 x - 8 \cdot - 8) - 27 = 0$

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 $x$ .

$3 (x^{2} + x \cdot - 8 - 8 x - 8 \cdot - 8) - 27 = 0$

Step 2.1.1.3.1.2

Move $- 8$ to the left of $x$ .

$3 (x^{2} - 8 \cdot x - 8 x - 8 \cdot - 8) - 27 = 0$

Step 2.1.1.3.1.3

Multiply $- 8$ by $- 8$ .

$3 (x^{2} - 8 x - 8 x + 64) - 27 = 0$

Step 2.1.1.3.2

Subtract $8 x$ from $- 8 x$ .

$3 (x^{2} - 16 x + 64) - 27 = 0$

Step 2.1.1.4

Apply the distributive property.

$3 x^{2} + 3 (- 16 x) + 3 \cdot 64 - 27 = 0$

Step 2.1.1.5

Simplify.

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Step 2.1.1.5.1

Multiply $- 16$ by $3$ .

$3 x^{2} - 48 x + 3 \cdot 64 - 27 = 0$

Step 2.1.1.5.2

Multiply $3$ by $64$ .

$3 x^{2} - 48 x + 192 - 27 = 0$

Step 2.1.2

Subtract $27$ from $192$ .

$3 x^{2} - 48 x + 165 = 0$

Step 2.2

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

$x = 5, 11$

Step 3