Find the value of c that makes x^2+26x+c a perfect-square trinomial.

Question

Find the value of c that makes x^2+26x+c a perfect-square trinomial.

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Kennedy 2 weeks 2021-11-19T12:10:15+00:00 1 Answer 0 views 0

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    2021-11-19T12:12:08+00:00

    c = 169

    square is (x + 13)^2

    Explanation:

    In the form:
    ax^2+ bx +c
    to complete the square a = 1 is required.
    c = (b/2)^2
    the square term is b/2
    x^2 + 26x + c
    a = 1 so we are okay to complete the square.
    b = 26
    c = (26/2)^2 = 13^2 = 169
    finally to complete the square:
    x^2 + 26x + 169 = (x+b/2)^2 = (x+13)^2

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