Basic Math Examples

$- n^{2} + 4 n - 10 = - 6$

Step 1

Add $6$ to both sides of the equation.

$- n^{2} + 4 n - 10 + 6 = 0$

Step 2

Add $- 10$ and $6$ .

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

Step 3

Factor the left side of the equation.

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Step 3.1

Factor $- 1$ out of $- n^{2} + 4 n - 4$ .

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Step 3.1.1

Factor $- 1$ out of $- n^{2}$ .

$- (n^{2}) + 4 n - 4 = 0$

Step 3.1.2

Factor $- 1$ out of $4 n$ .

$- (n^{2}) - (- 4 n) - 4 = 0$

Step 3.1.3

Rewrite $- 4$ as $- 1 (4)$ .

$- (n^{2}) - (- 4 n) - 1 \cdot 4 = 0$

Step 3.1.4

Factor $- 1$ out of $- (n^{2}) - (- 4 n)$ .

$- (n^{2} - 4 n) - 1 \cdot 4 = 0$

Step 3.1.5

Factor $- 1$ out of $- (n^{2} - 4 n) - 1 (4)$ .

$- (n^{2} - 4 n + 4) = 0$

Step 3.2

Factor using the perfect square rule.

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Step 3.2.1

Rewrite $4$ as $2^{2}$ .

$- (n^{2} - 4 n + 2^{2}) = 0$

Step 3.2.2

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

$4 n = 2 \cdot n \cdot 2$

Step 3.2.3

Rewrite the polynomial.

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

Step 3.2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = n$ and $b = 2$ .

$- {(n - 2)}^{2} = 0$

Step 4

Divide each term in $- {(n - 2)}^{2} = 0$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- {(n - 2)}^{2} = 0$ by $- 1$ .

$\frac{- {(n - 2)}^{2}}{- 1} = \frac{0}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{{(n - 2)}^{2}}{1} = \frac{0}{- 1}$

Step 4.2.2

Divide ${(n - 2)}^{2}$ by $1$ .

${(n - 2)}^{2} = \frac{0}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $- 1$ .

${(n - 2)}^{2} = 0$

Step 5

Set the $n - 2$ equal to $0$ .

$n - 2 = 0$

Step 6

Add $2$ to both sides of the equation.

$n = 2$