Solve the equation by completing the square. 8x2= -11x-7 ?

1 Answer
Roy Ø.
Jun 24, 2018

x=−1116±√1034i=−116(11±4√103i)

Explanation:

As 8x2 can be read as 8 times 2, I would advice you to write this as 8x^2 to ensure you are not misunderstood. This is 8x2

It's useful to start with drawing a graph:
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As the graph does not cross the x axis, this means the solutions are complex, something which is useful to know before we start.

As we want to complete the square, we write the expression as
8x2+11x=−11x−7+11x=−7
Divide all therms with 8:
x2+118x=−78

We want to write the left side on the form
(x+a)2=x2+2ax+a2
Therefore 2a=118 or a=1116
Add (1116)2=121162 to both sides to fulfill the square:
x2+2⋅1116x+(1116)2=−78+121162
=−7⋅32+121162=−103162
(x+1116)2=−103162

Therefore:
x+1116=√1034i
x=−116(11±4√103i)

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