Algebra Examples

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

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the right side.

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Step 1.1.1

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

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Step 1.1.1.1

Rewrite ${(2 x + 1)}^{2}$ as $(2 x + 1) (2 x + 1)$ .

$5 x = (2 x + 1) (2 x + 1)$

Step 1.1.1.2

Expand $(2 x + 1) (2 x + 1)$ using the FOIL Method.

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Step 1.1.1.2.1

Apply the distributive property.

$5 x = 2 x (2 x + 1) + 1 (2 x + 1)$

Step 1.1.1.2.2

Apply the distributive property.

$5 x = 2 x (2 x) + 2 x \cdot 1 + 1 (2 x + 1)$

Step 1.1.1.2.3

Apply the distributive property.

$5 x = 2 x (2 x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Step 1.1.1.3

Simplify and combine like terms.

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Step 1.1.1.3.1

Simplify each term.

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Step 1.1.1.3.1.1

Rewrite using the commutative property of multiplication.

$5 x = 2 \cdot 2 x \cdot x + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Step 1.1.1.3.1.2

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

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Step 1.1.1.3.1.2.1

Move $x$ .

$5 x = 2 \cdot 2 (x \cdot x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Step 1.1.1.3.1.2.2

Multiply $x$ by $x$ .

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

Step 1.1.1.3.1.3

Multiply $2$ by $2$ .

$5 x = 4 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Step 1.1.1.3.1.4

Multiply $2$ by $1$ .

$5 x = 4 x^{2} + 2 x + 1 (2 x) + 1 \cdot 1$

Step 1.1.1.3.1.5

Multiply $2 x$ by $1$ .

$5 x = 4 x^{2} + 2 x + 2 x + 1 \cdot 1$

Step 1.1.1.3.1.6

Multiply $1$ by $1$ .

$5 x = 4 x^{2} + 2 x + 2 x + 1$

Step 1.1.1.3.2

Add $2 x$ and $2 x$ .

$5 x = 4 x^{2} + 4 x + 1$

Step 1.2

Move all the expressions to the left side of the equation.

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Step 1.2.1

Subtract $4 x^{2}$ from both sides of the equation.

$5 x - 4 x^{2} = 4 x + 1$

Step 1.2.2

Subtract $4 x$ from both sides of the equation.

$5 x - 4 x^{2} - 4 x = 1$

Step 1.2.3

Subtract $1$ from both sides of the equation.

$5 x - 4 x^{2} - 4 x - 1 = 0$

Step 1.3

Subtract $4 x$ from $5 x$ .

$- 4 x^{2} + x - 1 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = - 4$ , $b = 1$ , $c = - 1$