Pre-Algebra Examples

$2 x^{2} - (x - 2) (x + 15) = 7 (x - 3)$

Step 1

Simplify $2 x^{2} - (x - 2) (x + 15)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 x^{2} + (- x - - 2) (x + 15) = 7 (x - 3)$

Step 1.1.2

Multiply $- 1$ by $- 2$ .

$2 x^{2} + (- x + 2) (x + 15) = 7 (x - 3)$

Step 1.1.3

Expand $(- x + 2) (x + 15)$ using the FOIL Method.

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Step 1.1.3.1

Apply the distributive property.

$2 x^{2} - x (x + 15) + 2 (x + 15) = 7 (x - 3)$

Step 1.1.3.2

Apply the distributive property.

$2 x^{2} - x \cdot x - x \cdot 15 + 2 (x + 15) = 7 (x - 3)$

Step 1.1.3.3

Apply the distributive property.

$2 x^{2} - x \cdot x - x \cdot 15 + 2 x + 2 \cdot 15 = 7 (x - 3)$

Step 1.1.4

Simplify and combine like terms.

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Step 1.1.4.1

Simplify each term.

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Step 1.1.4.1.1

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

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Step 1.1.4.1.1.1

Move $x$ .

$2 x^{2} - (x \cdot x) - x \cdot 15 + 2 x + 2 \cdot 15 = 7 (x - 3)$

Step 1.1.4.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} - x^{2} - x \cdot 15 + 2 x + 2 \cdot 15 = 7 (x - 3)$

Step 1.1.4.1.2

Multiply $15$ by $- 1$ .

$2 x^{2} - x^{2} - 15 x + 2 x + 2 \cdot 15 = 7 (x - 3)$

Step 1.1.4.1.3

Multiply $2$ by $15$ .

$2 x^{2} - x^{2} - 15 x + 2 x + 30 = 7 (x - 3)$

Step 1.1.4.2

Add $- 15 x$ and $2 x$ .

$2 x^{2} - x^{2} - 13 x + 30 = 7 (x - 3)$

Step 1.2

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

$x^{2} - 13 x + 30 = 7 (x - 3)$

Step 2

Simplify $7 (x - 3)$ .

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Step 2.1

Apply the distributive property.

$x^{2} - 13 x + 30 = 7 x + 7 \cdot - 3$

Step 2.2

Multiply $7$ by $- 3$ .

$x^{2} - 13 x + 30 = 7 x - 21$

Step 3

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

$x \approx 3, 17$

Step 4