Pre-Algebra Examples

$0 = 0.1 {(x + 5)}^{2} - 2.5$

Step 1

Simplify $0.1 {(x + 5)}^{2} - 2.5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x + 5)}^{2}$ as $(x + 5) (x + 5)$ .

$0 = 0.1 ((x + 5) (x + 5)) - 2.5$

Step 1.1.2

Expand $(x + 5) (x + 5)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$0 = 0.1 (x (x + 5) + 5 (x + 5)) - 2.5$

Step 1.1.2.2

Apply the distributive property.

$0 = 0.1 (x \cdot x + x \cdot 5 + 5 (x + 5)) - 2.5$

Step 1.1.2.3

Apply the distributive property.

$0 = 0.1 (x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5) - 2.5$

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 $x$ .

$0 = 0.1 (x^{2} + x \cdot 5 + 5 x + 5 \cdot 5) - 2.5$

Step 1.1.3.1.2

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

$0 = 0.1 (x^{2} + 5 \cdot x + 5 x + 5 \cdot 5) - 2.5$

Step 1.1.3.1.3

Multiply $5$ by $5$ .

$0 = 0.1 (x^{2} + 5 x + 5 x + 25) - 2.5$

Step 1.1.3.2

Add $5 x$ and $5 x$ .

$0 = 0.1 (x^{2} + 10 x + 25) - 2.5$

Step 1.1.4

Apply the distributive property.

$0 = 0.1 x^{2} + 0.1 (10 x) + 0.1 \cdot 25 - 2.5$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Multiply $0.1 (10 x)$ .

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Step 1.1.5.1.1

Multiply $10$ by $0.1$ .

$0 = 0.1 x^{2} + 1 x + 0.1 \cdot 25 - 2.5$

Step 1.1.5.1.2

Multiply $x$ by $1$ .

$0 = 0.1 x^{2} + x + 0.1 \cdot 25 - 2.5$

Step 1.1.5.2

Multiply $0.1$ by $25$ .

$0 = 0.1 x^{2} + x + 2.5 - 2.5$

Step 1.2

Combine the opposite terms in $0.1 x^{2} + x + 2.5 - 2.5$ .

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Step 1.2.1

Subtract $2.5$ from $2.5$ .

$0 = 0.1 x^{2} + x + 0$

Step 1.2.2

Add $0.1 x^{2} + x$ and $0$ .

$0 = 0.1 x^{2} + x$

Step 2

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

$x = - 10, 0$

Step 3