Question

please solve the equation, and show work:
4(x+1)^2=64

Answer 1

Divide each term in the equation by 4.
(4(x+1)^(2))/4=64/4


simplify the left and right-hand side of the equation by simplifying each term.
(x+1)^(2)=16

Take the square root of each side of the equation to setup the solution for x.
sqrt((x+1)^(2))=+-sqrt(16)

Remove the perfect root factor (x+1) under the radical to solve for x.
(x+1)=+-sqrt(16)
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Pull all perfect square roots out from under the radical. In this case, remove the 4 because it is a perfect square.
(x+1)=+-4
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First, substitute in the + portion of the +- to find the first solution.
(x+1)=4

x=-1+4

x=3
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Next, substitute in the - portion of the +- to find the second solution.
(x+1)=-4

x=-1-4

x=-5
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The complete solution is the result of both the + and - portions of the solution.
x=3,-5