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) About Me  (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) About Me  (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
x+-+17%2F8+=+sqrt%28-95%29%2F8
x+=+17%2F8+%2B+i%2Asqrt%2895%29%2F8
=======================
x+-+17%2F8+=+-sqrt%28-95%29%2F8
x+=+17%2F8+-+i%2Asqrt%2895%29%2F8
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-17x%2B24+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-17%29%5E2-4%2A4%2A24=-95.

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 - sqrt%28+95%29+=+9.74679434480896.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-17%2Ax%2B24+%29