SOLUTION: Solve equation x^2+2x+5=0 value of k that completes the square x^2+10x+k

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Question 77762This question is from textbook
: Solve equation
x^2+2x+5=0
value of k that completes the square
x^2+10x+k
 This question is from textbook

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
To solve for x, we need to use the quadratic formula:
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 -16 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 -16 is + or - .

The solution is

Here's your graph:


So our answer is
or
The value of k that completes the square will be equal to the square of half of 10, which looks like this




So our polynomial becomes

Notice how it can be factored to which is a perfect square
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Solve equation
x^2+2x+5=0
Use the quadratic formula to get:
x=[-2+-sqrt(4-4*5)]/2
x=[-2+-4i]/2
x= -1+2i ; or x = -1-2i
=======================
value of k that completes the square
x^2+10x+k
x^2+10x+(10/2)^2
=x^2+10x+25
k=25
==============
Cheers,
Stan H.

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