SOLUTION: How do you solve these four problems im really lost 3V^2+9V-54=0 6X^2-2x-4=0 2X^2-7x-12=0 11K^2+8k+9=0

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Question 860163: How do you solve these four problems im really lost
3V^2+9V-54=0
6X^2-2x-4=0
2X^2-7x-12=0
11K^2+8k+9=0
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
How do you solve these four problems im really lost
3V^2+9V-54=0
Divide by 3, make it easier
v^2 + 3v - 18 = 0
Factor it
(v+6)*(v-3) = 0
Product = 0 --> 1 of the factors is zero
v+6 = 0
v = -6
---
v-3 = 0
v = +3
========================
6X^2-2x-4=0
Similar to #1
========================
2X^2-7x-12=0
Can't be factored, use the quadratic equation
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=145 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4.76039864469807, -1.26039864469807. Here's your graph:

The solver always says it can be factored, ignore that.
========================
11K^2+8k+9=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 : .

The discriminant -332 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 -332 is + or - .

The solution is , or
Here's your graph:
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