Algebra Examples

$k^{2} + 8 k + 22 = 6$

Step 1

Subtract $6$ from both sides of the equation.

$k^{2} + 8 k + 22 - 6 = 0$

Step 2

Subtract $6$ from $22$ .

$k^{2} + 8 k + 16 = 0$

Step 3

Factor using the perfect square rule.

Tap for more steps...

Step 3.1

Rewrite $16$ as $4^{2}$ .

$k^{2} + 8 k + 4^{2} = 0$

Step 3.2

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

$8 k = 2 \cdot k \cdot 4$

Step 3.3

Rewrite the polynomial.

$k^{2} + 2 \cdot k \cdot 4 + 4^{2} = 0$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = k$ and $b = 4$ .

${(k + 4)}^{2} = 0$

Step 4

Set the $k + 4$ equal to $0$ .

$k + 4 = 0$

Step 5

Subtract $4$ from both sides of the equation.

$k = - 4$