Question

Complete the square 2m2−3m=−50

Answer 1

Completing the square answer

`\left(m - (3)/(4)\right)^2 = - (391)/(16)`

Solution set

`m = (3)/(4) + \frac{\sqrt[]{391}i}{4} = 0.75 + 4.94343 \, i`

`m = (3)/(4) - \frac{\sqrt[]{391}i}{4}` =
`0.75 - 4.94343 \, i`

Explanation:

Assuming the question is correctly interpreted as 2m2 = 2m², here is how to proceed

We have
`2m^2 - 3m =-50`

Divide by 2 on both sides

`m^2 - (3)/(2)m = - 25`

Take half of the coefficient of
`x` and square it

`\left[ - (3)/(2) \cdot (1)/(2) \right]^2 = (9)/(16)`

Add the result to both sides

`m^2 - (3)/(2)m + (9)/(16) = - 25 + (9)/(16)`

`m^2 - (3)/(2)m + (9)/(16)` can be re-written as a perfect square

`\left(m - (3)/(4)\right)^2`

The RHS becomes

`- 25 + (9)/(16) = ((-25)(16) + 9)/(9) = (-391)/(16)`

Therefore,

`\left(m - (3)/(4)\right)^2 = - (391)/(16)`

Take the square root of both side

`m - (3)/(4) = \pm \sqrt[]{ - (391)/(16)}`

Simplify

`m - (3)/(4) = \pm \frac{\sqrt[]{391}i}{4}`

Adding
`(3)/(4)` both sides

`m = (3)/(4) + \frac{\sqrt[]{391}i}{4}`

This gives the two solutions

`m= (3)/(4) + \frac{\sqrt[]{391}i}{4}` and

`m = (3)/(4) - \frac{\sqrt[]{391}i}{4}`

which becomes

`m = 0.75 + 4.94343 \, i` and

`m = 0.75 - 4.94343 \, i`