Which of the following is a solution of 4x2 = - 9x - 4?

The solution is - 0.609611 and - 1.64, I do not think you can simply find this by factoring but the only way is graphing it

Answer: The solutions are:

x1 = ( - 9 + √17) / 8 = - 0.6

x2 = (-9 - √17) / 8 = - 1.6

Step-by-step explanation:

We have the equation:

4*x^2 = - 9x - 4

first we put all the terms in one side of the equation:

4x^2 + 9x + 4 = 0

now, we use the Bhaskara's equation to find the roots:

where for a function:

ax^2 + bx + c = 0

the roots are:

x = (-b + - √ (b^2 - 4ac)) / 2a

where each root takes one of the possible signs of the square root.

so, in our case we have:

x = (-9 + - √ (9^2 - 4*4*4)) / (2*4) = ( - 9 + - √17) / 8

then the solutions are:

x1 = ( - 9 + √17) / 8 = - 0.6

x2 = (-9 - √17) / 8 = - 1.6