SOLUTION: 3x + 10 under the radical followed by = 5-2x i know the quadriatic formula should be used but im confused

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Question 78504: 3x + 10 under the radical followed by = 5-2x i know the quadriatic formula should be used but im confused
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x%2B10%29=5-2x
First, square both sides of the equation to get rid of that square root sign:
3x%2B10=%285-2x%29%5E2
Simplify the right side of the equation:
3x%2B10=25-20x%2B4x%5E2
Combine like terms and equate to zero:
4x%5E2-23x%2B15=0
Apply the quadratic formula:
x=%2823%2B-sqrt%2823%5E2-4%2A4%2A15%29%29%2F%282%2A4%29
Simplify:
x=%2823%2B-sqrt%28289%29%29%2F8
Simplify some more:
x=%2823%2B-17%29%2F8
This equation has two roots. Solve for x using the "+" condition
and the "-" condition separately. You get:
x=5 for the "+" case, and
x=3%2F4 for the "-" case
Now, this part is important...you need to plug these answers back in to
the original equation to be sure they are not "extraneous." An extraneous
root may be mathematically correct, but it is not the true answer. If you
plug x=5 back into the original equation, you will see that the equation
DOES NOT hold true. Hence, this is an extraneous root. If you plug 3/4 back
into the original equation, you will see that the equation DOES hold true,
so that one is your answer.