Finite Math Examples

$x^{2} - {(x - 2)}^{2} = 32$

Step 1

Subtract $32$ from both sides of the equation.

$x^{2} - {(x - 2)}^{2} - 32 = 0$

Step 2

Simplify $x^{2} - {(x - 2)}^{2} - 32$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$x^{2} - ((x - 2) (x - 2)) - 32 = 0$

Step 2.1.2

Expand $(x - 2) (x - 2)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$x^{2} - (x (x - 2) - 2 (x - 2)) - 32 = 0$

Step 2.1.2.2

Apply the distributive property.

$x^{2} - (x \cdot x + x \cdot - 2 - 2 (x - 2)) - 32 = 0$

Step 2.1.2.3

Apply the distributive property.

$x^{2} - (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2) - 32 = 0$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$x^{2} - (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2) - 32 = 0$

Step 2.1.3.1.2

Move $- 2$ to the left of $x$ .

$x^{2} - (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2) - 32 = 0$

Step 2.1.3.1.3

Multiply $- 2$ by $- 2$ .

$x^{2} - (x^{2} - 2 x - 2 x + 4) - 32 = 0$

Step 2.1.3.2

Subtract $2 x$ from $- 2 x$ .

$x^{2} - (x^{2} - 4 x + 4) - 32 = 0$

Step 2.1.4

Apply the distributive property.

$x^{2} - x^{2} - (- 4 x) - 1 \cdot 4 - 32 = 0$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $- 4$ by $- 1$ .

$x^{2} - x^{2} + 4 x - 1 \cdot 4 - 32 = 0$

Step 2.1.5.2

Multiply $- 1$ by $4$ .

$x^{2} - x^{2} + 4 x - 4 - 32 = 0$

Step 2.2

Subtract $x^{2}$ from $x^{2}$ .

$0 + 4 x - 4 - 32 = 0$

Step 2.3

Add $0$ and $4 x$ .

$4 x - 4 - 32 = 0$

Step 2.4

Subtract $32$ from $- 4$ .

$4 x - 36 = 0$

Step 3

Factor $4$ out of $4 x - 36$ .

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Step 3.1

Factor $4$ out of $4 x$ .

$4 (x) - 36 = 0$

Step 3.2

Factor $4$ out of $- 36$ .

$4 x + 4 \cdot - 9 = 0$

Step 3.3

Factor $4$ out of $4 x + 4 \cdot - 9$ .

$4 (x - 9) = 0$

Step 4

Divide each term in $4 (x - 9) = 0$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 (x - 9) = 0$ by $4$ .

$\frac{4 (x - 9)}{4} = \frac{0}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 (x - 9)}{4} = \frac{0}{4}$

Step 4.2.1.2

Divide $x - 9$ by $1$ .

$x - 9 = \frac{0}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $4$ .

$x - 9 = 0$

Step 5

Add $9$ to both sides of the equation.

$x = 9$