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

1 Answer
Roy Ø.
Jun 24, 2018

x=-11/16+-sqrt103/4i=-1/16(11+-4sqrt103i)

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 8x^2

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
8x^2+11x=-11x-7+11x=-7
Divide all therms with 8:
x^2+11/8x=-7/8

We want to write the left side on the form
(x+a)^2=x^2+2ax+a^2
Therefore 2a=11/8 or a=11/16
Add (11/16)^2=121/16^2 to both sides to fulfill the square:
x^2+2*11/16x+(11/16)^2=-7/8+121/16^2
=(-7*32+121)/16^2=(-103)/16^2
(x+11/16)^2=(-103)/16^2

Therefore:
x+11/16=sqrt103/4i
x=-1/16(11+-4sqrt103i)

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