SOLUTION: How would I solve this? Find all real solutions of each equation. Please help me solve this equation: {{{ 2 sqrt (x^2+3)= sqrt (-16x-3) }}}

Question 154730: How would I solve this?
Find all real solutions of each equation.
Please help me solve this equation:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!

Square both sides
4*(x^2 + 3) = -16x - 3
4x^2 + 12 = -16x - 3
4x^2 + 16x + 15 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=16 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1.5, -2.5. Here's your graph:

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