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

Question

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

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Thành Đạt 5 years 2021-08-19T12:46:10+00:00 1 Answers 14 views 0

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  1. linhdan
    0
    2021-08-19T12:47:26+00:00
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    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}

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )