Question

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

Answer 1

`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:

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)`