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30 August, 09:53

Find one value of x that is a solution to the equation

(7x+2) ^2+6 (7x+2) = 27

x=?

+2
Answers (2)
  1. 30 August, 10:27
    0
    x = - 11/7 and x = 1/7

    Step-by-step explanation:

    (7x+2) ^2+6 (7x+2) = 27

    Subtract 27 from each side

    (7x+2) ^2+6 (7x+2) - 27=0

    Let m = 7x+2

    m^2 + 6m - 27=0

    Factor

    (m+9) (m-3) = 0

    Using the zero product property

    m+9 = 0 m-3 = 0

    m=-9 m=3

    Substitute m = 7x+2 back in

    7x+2 = - 9 7x+2 = 3

    Subtract 2 from each side

    7x+2-2 = - 9-2 7x+2-2 = 3-2

    7x = - 11 7x = 1

    Divide by 7

    7x/7 = - 11/7 7x/7 = 1/7

    x = - 11/7 and x = 1/7
  2. 30 August, 12:58
    0
    x = 1/7 is one solution.

    Step-by-step explanation:

    (7x+2) ^2+6 (7x+2) = 27

    Let 7x + 2 = y, then we have the quadratic equation:-

    y^2 + 6y - 27 = 0

    (y + 9) (y - 3) = 0

    y = - 9, 3

    Substituting back for y:-

    7x + 2 = - 9

    7x = - 11

    x = - 11/7

    Also 7x + 2 = 3

    7x = 1

    x = 1/7

    Check if 1/7 fits the original equation:-

    ((7*-1/7 + 2) ^2 + 6 (7*1/7 + 2)

    = 9 + 18

    = 27 Checks OK.
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