Algebra Examples

4 n^{2} + 24 n + 25 = 4 n

$4 n^{2} + 24 n + 25 = 4 n$

Step 1

Move all terms containing

n

$n$ to the left side of the equation.

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Step 1.1

Subtract

4 n

$4 n$ from both sides of the equation.

4 n^{2} + 24 n + 25 - 4 n = 0

$4 n^{2} + 24 n + 25 - 4 n = 0$

Step 1.2

Subtract

4 n

$4 n$ from

24 n

$24 n$ .

4 n^{2} + 20 n + 25 = 0

$4 n^{2} + 20 n + 25 = 0$

4 n^{2} + 20 n + 25 = 0

$4 n^{2} + 20 n + 25 = 0$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite

4 n^{2}

$4 n^{2}$ as

{(2 n)}^{2}

${(2 n)}^{2}$ .

{(2 n)}^{2} + 20 n + 25 = 0

${(2 n)}^{2} + 20 n + 25 = 0$

Step 2.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

{(2 n)}^{2} + 20 n + 5^{2} = 0

${(2 n)}^{2} + 20 n + 5^{2} = 0$

Step 2.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

20 n = 2 \cdot (2 n) \cdot 5

$20 n = 2 \cdot (2 n) \cdot 5$

Step 2.4

Rewrite the polynomial.

{(2 n)}^{2} + 2 \cdot (2 n) \cdot 5 + 5^{2} = 0

${(2 n)}^{2} + 2 \cdot (2 n) \cdot 5 + 5^{2} = 0$

Step 2.5

Factor using the perfect square trinomial rule

a^{2} + 2 a b + b^{2} = {(a + b)}^{2}

$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where

a = 2 n

$a = 2 n$ and

b = 5

$b = 5$ .

{(2 n + 5)}^{2} = 0

${(2 n + 5)}^{2} = 0$

{(2 n + 5)}^{2} = 0

${(2 n + 5)}^{2} = 0$

Step 3

Set the

2 n + 5

$2 n + 5$ equal to

0

$0$ .

2 n + 5 = 0

$2 n + 5 = 0$

Step 4

Solve for

n

$n$ .

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Step 4.1

Subtract

5

$5$ from both sides of the equation.

2 n = - 5

$2 n = - 5$

Step 4.2

Divide each term in

2 n = - 5

$2 n = - 5$ by

2

$2$ and simplify.

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Step 4.2.1

Divide each term in

2 n = - 5

$2 n = - 5$ by

2

$2$ .

\frac{2 n}{2} = \frac{- 5}{2}

$\frac{2 n}{2} = \frac{- 5}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

2

$2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 n}{2} = \frac{- 5}{2}$

Step 4.2.2.1.2

Divide

$n$ by

$1$ .

$n = \frac{- 5}{2}$

$n = \frac{- 5}{2}$

$n = \frac{- 5}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$n = - \frac{5}{2}$

$n = - \frac{5}{2}$

$n = - \frac{5}{2}$

$n = - \frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{5}{2}$

Decimal Form:

$n = - 2.5$

Mixed Number Form:

$n = - 2 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$