Question 165055This 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.
CHECKING:
Let x = - 4.
sqrt{7x + 29} = x + 3....origiginal question
sqrt{7(-4) + 29} = (-4) + 3
sqrt{-28 + 29} = -1
sqrt{1} = -1
1 DOES NOT EQUAL -1.
We REJECT x = -4 because it is does not produce the same answer on both sides of the equation after checking.
Now, let x = 5 and do the same thing.
sqrt{7x + 29} = x + 3....original question
sqrt{7(5) + 29} = 5 + 3
sqrt{35 + 29} = 8
sqrt{64} = 8
8 = 8...It checks!!
The only TRUE answer here is x = 8
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