SOLUTION: find real solutions. {{{x+sqrt(x)=6}}} Thanks Caroline

Question 5225: find real solutions.

Thanks Caroline
Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
Caroline,
Try using y instead of . x is squared, or . So, your original equation becomes
. I will use my pluggable quadratic solver now:

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=25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2, -3. Here's your graph:

since y is sqrt(x), y cannot be negative, so solution -3 is invalid. You have y=2, y is , so x is 4.
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