SOLUTION: Help me solve each system by the substitution method: y=x^2-4x-10 y=-x^2-2x+14

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Question 169959: Help me solve each system by the substitution method:
y=x^2-4x-10
y=-x^2-2x+14
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Help me solve each system by the substitution method:
y=x^2-4x-10
y=-x^2-2x+14
------------
These are quadratics (2nd order eqns). I don't think substution applies.
y=x^2-4x-10
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=56 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 5.74165738677394, -1.74165738677394. Here's your graph:

It's
2 + sqrt(14)
2 - sqrt(14)
----------------
y=-x^2-2x+14
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 : .

The discriminant -52 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -52 is + or - .

The solution is , or
Here's your graph:

This one is:
1 + sqrt(-13)
1 - sqrt(-13)

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