Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

Question

Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

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    2021-09-10T03:48:06+00:00

    Answer:

    -12 and 2

    Step-by-step explanation:

    x^2+10x=24\\

    x^2+2*5*x=24

    x^2+2*5*x+5^2-5^2=24

    (x^2+2*5*x+5^2)-5^2=24

    Using the identity

    a^2+2*a*b+b^2 = (a+b)^2

    we get

    (x+5)^2-5^2=24

    (x+5)^2-25=24\\

    (x+5)^2=24+25\\(x+5)^2=49\\(x+5)=+7 \\or (x+5)=-7\\

    Solving both of them we get

    x=-12 or x=2

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