Question

Solve each equation by completing the square. n^2 - 6n + 6 = -2​

Answer 1

Step-by-step explanation

• Separate the constant out of expression.

`( {n}^(2) - 6n) + 6 = - 2`

• Find the constant that makes the expression able to be squared. You have to subtract the separated constant by new constant as well.

`( {n}^(2) - 6n + 9) + 6 - 9 = - 2 \\ {(n - 3)}^(2) - 3 = - 2 \\ {(n - 3)}^(2) = 1`

• Square Root both sides to get rid the squared expression. Make sure to write plus or minus.

`\sqrt{ {(n - 3)}^(2) } = + √(1) \\ \sqrt{ {(n - 3)}^(2) } = - √(1) \\ n - 3 = 1 \\ n - 3 = - 1`

`n - 3 = 1 \: \: \: or \: \: \: n - 3 = - 1 \\ n = 1 + 3 \: \: \: or \: \: \: n = - 1 + 3 \\ n = 4 \: \: \: or \: \: \: n = 2`

Answer

`\large \boxed {n = 4,2}`