n² + 14 = 12n how do I solve by quadratic formula ​

Question

n² + 14 = 12n
how do I solve by quadratic formula ​

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Cora 2 months 2021-09-27T12:13:03+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-27T12:14:03+00:00

    Answer:

    Step-by-step explanation:

    The quadratic formula is \frac{-b±\sqrt{b^{2}-4ac } }{2a}

    Ignore the weird A at the beginning, I don’t know why it is there.

    To get your equation into a quadratic equation, we have to move 12n to the other side, giving us

    n^{2} -12n+14

    So in this case, our a=1, b=-12, and c=14. Remember ax^{2}+bx+c

    So we plug these values into our formula

    \frac{12±\sqrt{144-4(14)} }{2}. Again, ignore the weird A.

    simplify and you will get

    \frac{12±\sqrt{88} }{2}

    simplify the square root and you get 2\sqrt{22}

    divide the 2\sqrt{22} and 12 by the 2 on the bottom and you will get \sqrt{22} and 6

    So your answers are 6-\sqrt{22} and 6+\sqrt{22}

    0
    2021-09-27T12:14:25+00:00

    Answer:

    n = 6 + \sqrt{22}  or  n = 6 – \sqrt{22}

    Step-by-step explanation:

    We can solve this equation using the quadratic formula OR Completing the Square method.

    n² + 14 = 12n

    rearrange :  n² – 12n + 14  = 0  

    here  a= 1 , b = -12,  c = 14

    the quadratic formula says:   x =  – b/ (2a)  +  root(b^2 – 4ac) / (2a)

    or  x =  – b/ (2a)  –  root(b^2 – 4ac) / (2a)

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

    x = 6  +  root (144 – 56) / 2

    x = 6 + root(88)/2

    x = 6 + root(4*22) / 2

    x = 6 + 2*root(22)/2

    x = 6 + root(22)  = 6 + \sqrt{22}

    so   x =6 + \sqrt{22}   or  x = 6 – \sqrt{22}

    In this case  x = n

    n = 6 + \sqrt{22}  or  n = 6 – \sqrt{22}

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