What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve.

Question

What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve.

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Luna 2 months 2021-10-06T19:27:17+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-06T19:28:25+00:00

    Answer:

    x = -8 + 5 \sqrt{2}  or  x = -8 – 5\sqrt{2}

    Step-by-step explanation:

    let u = x + 2

    then  (x + 2)2 + 12(x + 2) – 14 = 0 becomes:

    u^2 + 12*u  – 14  = 0

    Quadratic Formula:    u = -b/(2a) +  root(b^2  – 4ac) / (2a)

    u = -12/(2)  +  root (12^2 – 4*(-14) ) /(2)

    u = -6  +  root( 144 + 56) / 2

    u = -6 +  root(200)/2

    u = -6 + 5 root(2)

    or u = -6 – 5root(2)

    replace u = x + 2

    x + 2 = -6 + 5root(2)

    x = -8 + 5 root(2)  or  x = -8 – 5root(2)

    —————-

    Do Completing the Square:

    u^2  + 12 u + 36 – 36 – 14 = 0

    (u + 6)^2 – 50 = 0

    (u + 6)^2 = 50

    u + 6 = root(50)

    u = -6 + 5root(2)  OR    u = -6 – 5root(2)

    0
    2021-10-06T19:28:44+00:00

    Answer:

    A

    Step-by-step explanation:

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45:7+7-4:2-5:5*4+35:2 =? ( )