Pre-Algebra Examples

$2 (x + 5) (x - 2) = x (x + 5) + 70$

Step 1

Simplify $2 (x + 5) (x - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (x + 5) (x - 2) = x (x + 5) + 70$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$(2 x + 2 \cdot 5) (x - 2) = x (x + 5) + 70$

Step 1.2.2

Multiply $2$ by $5$ .

$(2 x + 10) (x - 2) = x (x + 5) + 70$

Step 1.3

Expand $(2 x + 10) (x - 2)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$2 x (x - 2) + 10 (x - 2) = x (x + 5) + 70$

Step 1.3.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 2 + 10 (x - 2) = x (x + 5) + 70$

Step 1.3.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 2 + 10 x + 10 \cdot - 2 = x (x + 5) + 70$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

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

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Step 1.4.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 2 + 10 x + 10 \cdot - 2 = x (x + 5) + 70$

Step 1.4.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 2 + 10 x + 10 \cdot - 2 = x (x + 5) + 70$

Step 1.4.1.2

Multiply $- 2$ by $2$ .

$2 x^{2} - 4 x + 10 x + 10 \cdot - 2 = x (x + 5) + 70$

Step 1.4.1.3

Multiply $10$ by $- 2$ .

$2 x^{2} - 4 x + 10 x - 20 = x (x + 5) + 70$

Step 1.4.2

Add $- 4 x$ and $10 x$ .

$2 x^{2} + 6 x - 20 = x (x + 5) + 70$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$2 x^{2} + 6 x - 20 = x \cdot x + x \cdot 5 + 70$

Step 2.2

Multiply $x$ by $x$ .

$2 x^{2} + 6 x - 20 = x^{2} + x \cdot 5 + 70$

Step 2.3

Move $5$ to the left of $x$ .

$2 x^{2} + 6 x - 20 = x^{2} + 5 x + 70$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $x^{2}$ from both sides of the equation.

$2 x^{2} + 6 x - 20 - x^{2} = 5 x + 70$

Step 3.2

Subtract $5 x$ from both sides of the equation.

$2 x^{2} + 6 x - 20 - x^{2} - 5 x = 70$

Step 3.3

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

$x^{2} + 6 x - 20 - 5 x = 70$

Step 3.4

Subtract $5 x$ from $6 x$ .

$x^{2} + x - 20 = 70$

Step 4

Subtract $70$ from both sides of the equation.

$x^{2} + x - 20 - 70 = 0$

Step 5

Subtract $70$ from $- 20$ .

$x^{2} + x - 90 = 0$

Step 6

Factor $x^{2} + x - 90$ using the AC method.

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Step 6.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 90$ and whose sum is $1$ .

$- 9, 10$

Step 6.2

Write the factored form using these integers.

$(x - 9) (x + 10) = 0$

Step 7

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 9 = 0$

$x + 10 = 0$

Step 8

Set $x - 9$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Step 8.2

Add $9$ to both sides of the equation.

$x = 9$

Step 9

Set $x + 10$ equal to $0$ and solve for $x$ .

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Step 9.1

Set $x + 10$ equal to $0$ .

$x + 10 = 0$

Step 9.2

Subtract $10$ from both sides of the equation.

$x = - 10$

Step 10

The final solution is all the values that make $(x - 9) (x + 10) = 0$ true.

$x = 9, - 10$