SOLUTION: I home school and I am stuck on a problem. all the information the directions give me is "solve each equation" The worksheet is on radical equations' graphs, and complex numbers

Algebra ->  Equations -> SOLUTION: I home school and I am stuck on a problem. all the information the directions give me is "solve each equation" The worksheet is on radical equations' graphs, and complex numbers       Log On


   

Question 192161: I home school and I am stuck on a problem.
all the information the directions give me is "solve each equation"
The worksheet is on radical equations' graphs, and complex numbers
Please help me solve this equation:
(2x-3)^2=-24
Found 2 solutions by Mathtut, RAY100:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-3%29%282x-3%29=-24
:
4x%5E2-6x-6x%2B9=-24
:
4x%5E2-12x%2B36=0
:
4%28x%5E2-3x%2B9%29=0
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B9+=+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=%28-3%29%5E2-4%2A1%2A9=-27.

The discriminant -27 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 -27 is + or - sqrt%28+27%29+=+5.19615242270663.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B9+%29

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
(2x-3)^2=24
take sq rt of both sides
2x-3 = sq rt 24 = +- (4.899)
2x-3 =+4.899
2x = 7.899
x= 3.95
or 2x-3= -4.899
2x = -1.899
x=-.95
checking
(2(3.95) -3 )^2= 24 ok
( 2(-.95) -3)^2 =24 ok