Pre-Algebra Examples

${(x - 3)}^{2} - x (x + 2) = 21$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$(x - 3) (x - 3) - x (x + 2) = 21$

Step 1.1.2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$x (x - 3) - 3 (x - 3) - x (x + 2) = 21$

Step 1.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 (x - 3) - x (x + 2) = 21$

Step 1.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 - x (x + 2) = 21$

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 $x$ .

$x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 - x (x + 2) = 21$

Step 1.1.3.1.2

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 - x (x + 2) = 21$

Step 1.1.3.1.3

Multiply $- 3$ by $- 3$ .

$x^{2} - 3 x - 3 x + 9 - x (x + 2) = 21$

Step 1.1.3.2

Subtract $3 x$ from $- 3 x$ .

$x^{2} - 6 x + 9 - x (x + 2) = 21$

Step 1.1.4

Apply the distributive property.

$x^{2} - 6 x + 9 - x \cdot x - x \cdot 2 = 21$

Step 1.1.5

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.5.1

Move $x$ .

$x^{2} - 6 x + 9 - (x \cdot x) - x \cdot 2 = 21$

Step 1.1.5.2

Multiply $x$ by $x$ .

$x^{2} - 6 x + 9 - x^{2} - x \cdot 2 = 21$

Step 1.1.6

Multiply $2$ by $- 1$ .

$x^{2} - 6 x + 9 - x^{2} - 2 x = 21$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $x^{2} - 6 x + 9 - x^{2} - 2 x$ .

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Step 1.2.1.1

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

$- 6 x + 9 + 0 - 2 x = 21$

Step 1.2.1.2

Add $- 6 x + 9$ and $0$ .

$- 6 x + 9 - 2 x = 21$

Step 1.2.2

Subtract $2 x$ from $- 6 x$ .

$- 8 x + 9 = 21$

Step 2

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

$x = - \frac{3}{2}$

Step 3