Question 165065This question is from textbook Elementary and Intermediate
: 96.) Find all real or imaginary solutions. use the method of your choice.
sqrt(7x+29=x+3)
This question is from textbook Elementary and Intermediate
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website!
sqrt{7x + 29} = x+3
There is nothing to move over as the radical symbol is isolated already.
We square both sides:
(sqrt{7x + 29})^2 = (x+3)^2
7x + 29 = (x+3) (x+3)
7x + 29 = x^2 + 6x + 9
Bring the entire left side to the right side and set entire equation to = 0.
x^2 + 6x + 9 - 7x - 29 = 0
We now combine like terms.
x^2 - x - 20 = 0
We factor this quadratic equation.
(x + 4) (x - 5) = 0
Set each factor to = 0 and solve for x.
x + 4 = 0
x = -4
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x - 5 = 0
x = 5
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We have two answers for x: x = -4 and x = 5 but are they both acceptable answers? In other words, if we replace x in the original equation with -4 and 5, will the answer be the same on both sides of the equation?
The only way to know is by CHECKING.
I'll let you do that.
Go back to your original radical equation, which is
sqrt{7x + 29} = x+3 and first replace x with -4 and simpllify and then replace x with 5 and simplify.
Whichever gives you the same answer on both sides of the equation will be the correct answer. It could also be the case that both answers for x are correct but checking is the only way to know for sure.
If you need help, write back.
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