SOLUTION: whats the answer for x^2+4x+10=3

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Question 761441: whats the answer for x^2+4x+10=3
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: X%5E2+%2B+4X+%2B+10+=+3
Set the equation to 0 by subtracting 3 from both sides
X%5E2+%2B+4X+%2B+10+-+3+=+3+-+3
Simplify
X%5E2+%2B+4X+%2B+7+=+0
You can now use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aX%5E2%2BbX%2Bc=0 (in our case 1X%5E2%2B4X%2B7+=+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=%284%29%5E2-4%2A1%2A7=-12.

The discriminant -12 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 -12 is + or - sqrt%28+12%29+=+3.46410161513775.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B7+%29

Since the discriminant is less than 0, there are no solutions without using imaginary numbers. This is why the graph never touches the X-axis.