Precalculus Examples

$3 {(x - 1)}^{2} - 162 = 0$

Step 1

Simplify $3 {(x - 1)}^{2} - 162$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$3 ((x - 1) (x - 1)) - 162 = 0$

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.

$3 (x (x - 1) - 1 (x - 1)) - 162 = 0$

Step 1.1.2.2

Apply the distributive property.

$3 (x \cdot x + x \cdot - 1 - 1 (x - 1)) - 162 = 0$

Step 1.1.2.3

Apply the distributive property.

$3 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) - 162 = 0$

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 $x$ .

$3 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) - 162 = 0$

Step 1.1.3.1.2

Move $- 1$ to the left of $x$ .

$3 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) - 162 = 0$

Step 1.1.3.1.3

Rewrite $- 1 x$ as $- x$ .

$3 (x^{2} - x - 1 x - 1 \cdot - 1) - 162 = 0$

Step 1.1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$3 (x^{2} - x - x - 1 \cdot - 1) - 162 = 0$

Step 1.1.3.1.5

Multiply $- 1$ by $- 1$ .

$3 (x^{2} - x - x + 1) - 162 = 0$

Step 1.1.3.2

Subtract $x$ from $- x$ .

$3 (x^{2} - 2 x + 1) - 162 = 0$

Step 1.1.4

Apply the distributive property.

$3 x^{2} + 3 (- 2 x) + 3 \cdot 1 - 162 = 0$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x + 3 \cdot 1 - 162 = 0$

Step 1.1.5.2

Multiply $3$ by $1$ .

$3 x^{2} - 6 x + 3 - 162 = 0$

Step 1.2

Subtract $162$ from $3$ .

$3 x^{2} - 6 x - 159 = 0$

Step 2

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

$x \approx - 6.34846922, 8.34846922$

Step 3