SOLUTION: square root 7x+29=x+3

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Question 103833: square root 7x+29=x+3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%287x%2B29%29=x%2B3 Start with the given equation


7x%2B29=%28x%2B3%29%5E2 Square both sides


7x%2B29=x%5E2%2B6x%2B9 Foil


0=x%5E2-x-20 Get all terms to one side

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-x-20=0 ( notice a=1, b=-1, and c=-20)





x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A-20+%29%29%2F%282%2A1%29 Plug in a=1, b=-1, and c=-20




x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A-20+%29%29%2F%282%2A1%29 Negate -1 to get 1




x+=+%281+%2B-+sqrt%28+1-4%2A1%2A-20+%29%29%2F%282%2A1%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)




x+=+%281+%2B-+sqrt%28+1%2B80+%29%29%2F%282%2A1%29 Multiply -4%2A-20%2A1 to get 80




x+=+%281+%2B-+sqrt%28+81+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%281+%2B-+9%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%281+%2B-+9%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%281+%2B+9%29%2F2 or x+=+%281+-+9%29%2F2


Lets look at the first part:


x=%281+%2B+9%29%2F2


x=10%2F2 Add the terms in the numerator

x=5 Divide


So one answer is

x=5




Now lets look at the second part:


x=%281+-+9%29%2F2


x=-8%2F2 Subtract the terms in the numerator

x=-4 Divide


So another answer is

x=-4


So our solutions are:

x=5 or x=-4





Now let's plug in our possible answers back in to check



Let's check the answer x=-4

sqrt%287x%2B29%29=x%2B3 Start with the given equation


sqrt%287%28-4%29%2B29%29=-4%2B3 Plug in x=-4


1=-1 Simplify. Since this is not true, x=-4 is not a solution




Now let's check the answer x=5

sqrt%287x%2B29%29=x%2B3 Start with the given equation


sqrt%287%285%29%2B29%29=5%2B3 Plug in x=5


8=8 Simplify. Since this is true, x=5 is a solution



So our only solution is x=5