Question

What are the solutions of 4x2 + x = −3?

Select one:

Answer 1

Answer: C

Explanation: I just took the test and got it right <3

Answer 2

The correct answer is c.

Explanation:

Given the equation

`ax^(2)+bx+c=0`

The quadratic equation solves the values of ''x'' which satisfy the original equation (In the equation I replace ± by the symbol |):

`\frac{-b|\sqrt{b^(2)-4ac}}{2a}`

The solutions of
`4x^(2)+x=-3` are the same that the solutions of
`4x^(2)+x+3=0`

With
`a=4\\b=1\\c=3` we replace this in the quadratic equation ⇒

`\frac{-1|\sqrt{(1)^(2)-4(4)(3)}}{(2)(4)}` ⇒

`(-1|√(1-48))/(8)` ⇒

`(-1|√(-47))/(8)`

Given that
`i^(2)=-1` (imaginary numbers property)

`\frac{-1|\sqrt{47i^(2)}}{8}=(-1|i√(47))/(8)`

The solutions are
`(-1+i√(47))/(8)`

and
`(-1-i√(47))/(8)`

The correct answer is c.