SOLUTION: Solve 4x^2+6x+10 =0 expressing the result in simplest a+bi form. I tried to solve for x but no factors would be able to make a positive 6 and 10. Then I tried completing the square

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Question 868671: Solve 4x^2+6x+10 =0 expressing the result in simplest a+bi form. I tried to solve for x but no factors would be able to make a positive 6 and 10. Then I tried completing the square but I couldn't work it out. Maybe I did it wrong. Thanks a lot
Found 2 solutions by rothauserc, richwmiller:
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
4x^2+6x+10 = 0
divide both sides of the = by 2
2x^2 +3x +5 = 0
use quadratic formula
x = (-3 + square root(9 - 4*2*5)) / 4 = ( -3 + square root (-31)) / 4
x = (-3 - square root(9 - 4*2*5)) / 4 = ( -3 - square root (-31)) / 4
note that the square root of (-31) = square root of 31 times i where i = square root of -1, therefore
x = (-3 + 5.57i) / 4 = -0.75 + 5.57i/4 = -0.75 + 1.39i
x = (-3 - 5.57i) / 4 = -0.75 - 1.39i

Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
4x^2+6x+10 =0
2x^2+3x+5 =0

Solved by pluggable solver: SOLVE quadratic equation with variable

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 -31 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 -31 is + or - .

The solution is

Here's your graph: