Finite Math Examples

$3 x - {(5 x + 2)}^{2} = 47 - 25 x^{2}$

Step 1

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

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Step 1.1

Add $25 x^{2}$ to both sides of the equation.

$3 x - {(5 x + 2)}^{2} + 25 x^{2} = 47$

Step 1.2

Simplify each term.

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Step 1.2.1

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

$3 x - ((5 x + 2) (5 x + 2)) + 25 x^{2} = 47$

Step 1.2.2

Expand $(5 x + 2) (5 x + 2)$ using the FOIL Method.

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Step 1.2.2.1

Apply the distributive property.

$3 x - (5 x (5 x + 2) + 2 (5 x + 2)) + 25 x^{2} = 47$

Step 1.2.2.2

Apply the distributive property.

$3 x - (5 x (5 x) + 5 x \cdot 2 + 2 (5 x + 2)) + 25 x^{2} = 47$

Step 1.2.2.3

Apply the distributive property.

$3 x - (5 x (5 x) + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2) + 25 x^{2} = 47$

Step 1.2.3

Simplify and combine like terms.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Rewrite using the commutative property of multiplication.

$3 x - (5 \cdot 5 x \cdot x + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2) + 25 x^{2} = 47$

Step 1.2.3.1.2

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

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Step 1.2.3.1.2.1

Move $x$ .

$3 x - (5 \cdot 5 (x \cdot x) + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2) + 25 x^{2} = 47$

Step 1.2.3.1.2.2

Multiply $x$ by $x$ .

$3 x - (5 \cdot 5 x^{2} + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2) + 25 x^{2} = 47$

Step 1.2.3.1.3

Multiply $5$ by $5$ .

$3 x - (25 x^{2} + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2) + 25 x^{2} = 47$

Step 1.2.3.1.4

Multiply $2$ by $5$ .

$3 x - (25 x^{2} + 10 x + 2 (5 x) + 2 \cdot 2) + 25 x^{2} = 47$

Step 1.2.3.1.5

Multiply $5$ by $2$ .

$3 x - (25 x^{2} + 10 x + 10 x + 2 \cdot 2) + 25 x^{2} = 47$

Step 1.2.3.1.6

Multiply $2$ by $2$ .

$3 x - (25 x^{2} + 10 x + 10 x + 4) + 25 x^{2} = 47$

Step 1.2.3.2

Add $10 x$ and $10 x$ .

$3 x - (25 x^{2} + 20 x + 4) + 25 x^{2} = 47$

Step 1.2.4

Apply the distributive property.

$3 x - (25 x^{2}) - (20 x) - 1 \cdot 4 + 25 x^{2} = 47$

Step 1.2.5

Simplify.

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Step 1.2.5.1

Multiply $25$ by $- 1$ .

$3 x - 25 x^{2} - (20 x) - 1 \cdot 4 + 25 x^{2} = 47$

Step 1.2.5.2

Multiply $20$ by $- 1$ .

$3 x - 25 x^{2} - 20 x - 1 \cdot 4 + 25 x^{2} = 47$

Step 1.2.5.3

Multiply $- 1$ by $4$ .

$3 x - 25 x^{2} - 20 x - 4 + 25 x^{2} = 47$

Step 1.3

Combine the opposite terms in $3 x - 25 x^{2} - 20 x - 4 + 25 x^{2}$ .

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Step 1.3.1

Add $- 25 x^{2}$ and $25 x^{2}$ .

$3 x - 20 x - 4 + 0 = 47$

Step 1.3.2

Add $3 x - 20 x - 4$ and $0$ .

$3 x - 20 x - 4 = 47$

Step 1.4

Subtract $20 x$ from $3 x$ .

$- 17 x - 4 = 47$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $4$ to both sides of the equation.

$- 17 x = 47 + 4$

Step 2.2

Add $47$ and $4$ .

$- 17 x = 51$

Step 3

Divide each term in $- 17 x = 51$ by $- 17$ and simplify.

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Step 3.1

Divide each term in $- 17 x = 51$ by $- 17$ .

$\frac{- 17 x}{- 17} = \frac{51}{- 17}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 17$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 17 x}{- 17} = \frac{51}{- 17}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{51}{- 17}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $51$ by $- 17$ .

$x = - 3$