Algebra Examples

$x + {(5 x + 2)}^{2} = 25 (1 + x^{2})$

Step 1

Simplify $25 (1 + x^{2})$ .

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Step 1.1

Apply the distributive property.

$x + {(5 x + 2)}^{2} = 25 \cdot 1 + 25 x^{2}$

Step 1.2

Multiply $25$ by $1$ .

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

Step 2

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

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Step 2.1

Subtract $25 x^{2}$ from both sides of the equation.

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

Step 2.2

Simplify each term.

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Step 2.2.1

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

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

Step 2.2.2

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

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Step 2.2.2.1

Apply the distributive property.

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

Step 2.2.2.2

Apply the distributive property.

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

Step 2.2.2.3

Apply the distributive property.

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

Step 2.2.3

Simplify and combine like terms.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.2.3.1.2

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

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Step 2.2.3.1.2.1

Move $x$ .

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

Step 2.2.3.1.2.2

Multiply $x$ by $x$ .

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

Step 2.2.3.1.3

Multiply $5$ by $5$ .

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

Step 2.2.3.1.4

Multiply $2$ by $5$ .

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

Step 2.2.3.1.5

Multiply $5$ by $2$ .

$x + 25 x^{2} + 10 x + 10 x + 2 \cdot 2 - 25 x^{2} = 25$

Step 2.2.3.1.6

Multiply $2$ by $2$ .

$x + 25 x^{2} + 10 x + 10 x + 4 - 25 x^{2} = 25$

Step 2.2.3.2

Add $10 x$ and $10 x$ .

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

Step 2.3

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

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Step 2.3.1

Subtract $25 x^{2}$ from $25 x^{2}$ .

$x + 20 x + 4 + 0 = 25$

Step 2.3.2

Add $x + 20 x + 4$ and $0$ .

$x + 20 x + 4 = 25$

Step 2.4

Add $x$ and $20 x$ .

$21 x + 4 = 25$

Step 3

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

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Step 3.1

Subtract $4$ from both sides of the equation.

$21 x = 25 - 4$

Step 3.2

Subtract $4$ from $25$ .

$21 x = 21$

Step 4

Divide each term in $21 x = 21$ by $21$ and simplify.

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Step 4.1

Divide each term in $21 x = 21$ by $21$ .

$\frac{21 x}{21} = \frac{21}{21}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $21$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{21 x}{21} = \frac{21}{21}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{21}{21}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $21$ by $21$ .

$x = 1$