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

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asked Sep 19, 2022 122k views

1 Answer

Eli Harold · Answer 1 · 2022-09-24T18:47:30+0000

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

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.

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

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

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