SOLUTION: Hi, I'm reviewing for a test and I'm having serious problems with radicals. I've shown my progress thus far, which may or may not be correct. sqrt(15x + 4) = 4 - sqrt(2x + 3)

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Question 359998: Hi, I'm reviewing for a test and I'm having serious problems with radicals. I've
shown my progress thus far, which may or may not be correct.
sqrt(15x + 4) = 4 - sqrt(2x + 3)
square both sides:
15x + 4 = 16 - 8sqrt(2x + 3) + 2x + 3
simplify and gather like terms, then square both sides again (?)
(13x - 15)^2 = (-8sqrt(2x + 3)^2
The teacher gave us the answer of 11/169 and when finishing the problem like this, my answer was far off. Could you please walk me through this problem so I understand the steps? Thank you so much for your help :-)
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
sqrt(15x + 4) = 4 - sqrt(2x + 3)
15x+4=-8sqrt(2x+3)+2x+19
13x-15=-8sqrt(2x+3)
You should have finished the problem; you were correct so far.
169x^2-390x+225=128x+192
169x^2-518x+33=0
x=11/169 is the only answer to this problem.Quadratic equation.(see below)
.
Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=246016 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, 0.0650887573964497. Here's your graph:
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