Solve the equation by completing the square. x2 + 16x = 7

Question

Solve the equation by completing the square. x2 + 16x = 7

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Kaylee 3 weeks 2021-11-06T16:29:21+00:00 1 Answer 0 views 0

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    2021-11-06T16:30:26+00:00

    Answer:

    x = +\sqrt{71} - 8 , –\sqrt{71} - 8

    x ≈ .426, -16.426

    Step-by-step explanation:

    When we complete the square, we add a value to both sides to make the left side a “perfect square” that we can simplify to (a+b)^2.

    x^2 + 16x = 7

    x^2 + 16x + _____ = 7 + ______

    What do we put in the blank? The formula is to take half of b, then square that. Half of 16 is 8, 8^2 is 64, so

    x^2 + 16x + 64 = 7 + 64

    Now on the left side we have a perfect square!

    (x+8)^2 = 71

    Now all that’s left to do is simplify this to get x. First take the square root of both sides.

    x+8 = \sqrt{71}

    x = +\sqrt{71} - 8 , –\sqrt{71} - 8

    x ≈ .426, -16.426

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