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
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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)
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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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