Question

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

Answer 1

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.

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

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

Answer

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