Solve x^2 -6x=-5 by completing the square. Show all work for the steps below. (a) For x^2 -6x+c+-5+c, what value of c is used to complete th

Question

Solve x^2 -6x=-5 by completing the square. Show all work for the steps below. (a) For x^2 -6x+c+-5+c, what value of c is used to complete the square? (b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. (c) Solve for x

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Khánh Gia 4 years 2021-08-29T00:17:55+00:00 1 Answers 25 views 0

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  1. haidang
    0
    2021-08-29T00:19:51+00:00
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    x^2 – 6x = -5

    To complete the square we are going to rewrite the equation to a quadratic equation in the form:

    ax² + bx + c

    To do this we are going to transpose.

    x² – 6x = -5
    x² – 6x + 5 = 0

    Now we are going to rewrite the new equation in the form

    a(x + h)² + k

    Where a = 1
    h = 6x
    k = 5

    1(x² – 6x) + 5 = 0
    1(x² – 6x/2 + 3²) + 5 = 0, to find h, divide it by 2 then square the quotient and add it to the equation.

    1(x² – 3x + 9) + 5 – 9 = 0, to find k, subtract the square rooted quotient after multiplying it by a.

    1(x – 3)²- 4 = 0

    Now we solve.

    1(x – 3)² – 4 = 0
    1(x – 3)² = 4
    ±√1(x – 3)² = ±√4
    (x – 3) = √4 or (x – 3) = -√4
    x = 5 or x = 1

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