SOLUTION: Please help me solve this equation: sqrt(2x+11)-sqrt(x+9)=sqrt(x-6)

Question 1050203: Please help me solve this equation:
sqrt(2x+11)-sqrt(x+9)=sqrt(x-6)
Found 2 solutions by advanced_Learner, ikleyn:
Answer by advanced_Learner(501) (Show Source): You can put this solution on YOUR website!
-=

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-**=

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=*
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simplify
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thanks to quadratic solver

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=4624 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -10. Here's your graph:

Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.
Of the two roots x = 7 and x = -10, only the root x = 7 satisfies the original equation.

The other root, x = -10, is extraneous and does not satisfies the original equation.

Plots y = (red) and y = (green)

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