Solve this quadratic equation by completing the square. x^2 + 6x = 18

Question

Solve this quadratic equation by completing the square.

x^2 + 6x = 18

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Helga 3 years 2021-08-20T22:13:44+00:00 2 Answers 27 views 0

Answers ( )

  1. huyenthanh
    0
    2021-08-20T22:14:49+00:00
    Reply

    Step-by-step explanation:

    Use formula

    (\frac{b}{2} ) {}^{2}

    To add a third new term and factor to find the answer. Example

    x {}^{2} + 6x = 18

    ( \frac{6}{2} ) {}^{2}

    Which equal 9. so our equation look like

    {x}^{2} + 6x + 9 = 18 + 9

    The only number that multiply to 9 and add up to 6 is 3. So we write our equation like this.

    (x + 3) {}^{2} = 27

    Take the sqr root of both sides

    x + 3 = \sqrt{27}

    Subtract 3 from both sides

    x = \sqrt{27} - 3

    Since a sqr root of a number can be positive or negative, the answer is

    \sqrt{27} - 3

    or

    - ( \sqrt{27} ) - 3

  2. kimchi2
    0
    2021-08-20T22:15:04+00:00
    Reply

    Answer:

    Step-by-step explanation:

    x²+6x = 18

    coefficient of the x term:  6

    divide it in half:  3

    square it:  3²

    add 3² to both sides to complete the square and keep the equation balanced:

    x²+6x+3² = 18+3²

    (x+3)² = 27

    x+3 = ±√27 = ±3√3

    x = -3±3√3

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