SOLUTION: Solve the equation by completing the square: 4x^2 - 17x + 24 = 0

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Question 742354: Solve the equation by completing the square: 4x^2 - 17x + 24 = 0
Found 2 solutions by lenny460, Alan3354:
Answer by lenny460(1073)   (Show Source): You can put this solution on YOUR website!
Solve the equation by completing the square: 4x^2 - 17x + 24 = 0

The above trinomial is prime. It cannot be solved or factored.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the equation by completing the square: 4x^2 - 17x + 24 = 0
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4x^2 - 17x + 24 = 0
4x^2 - 17x = -24
x^2 - (17/4)x = -6
c to added = (b/2a)^2 = (17/8)^2
c = 289/64
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x^2 - (17/4)x + 289/64 = -6 + 289/64 = -95/64
(x - 17/8)^2 = -95/64


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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 -95 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 -95 is + or - .

The solution is , or
Here's your graph:
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