what is the solution of the quadratic equation 2x^2-x-14=0?

2x^2 - x - 14 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 2
b = -1
c = -14

x = [1 ±√(1 + 112)]/4
x = [1 ±√113]/4

∴ x = [1 ±√113]/4

Question Number 1 :
For this equation 2*x^2 - x - 14 = 0 , answer the following questions :
A. Find the roots using Quadratic Formula !
B. Use completing the square to find the root of the equation !

Answer Number 1 :
The equation 2*x^2 - x - 14 = 0 is already in a*x^2+b*x+c=0 form.
So we can imply that the value of a = 2, b = -1, c = -14.

1A. Find the roots using Quadratic Formula !
Use the formula,
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
We had know that a = 2, b = -1 and c = -14,
then the value a,b and c in the abc formula, can be subtituted.
Which produce x1 = (-(-1) + sqrt( (-1)^2 - 4 * (2)*(-14)))/(2*2) and x2 = (-(-1) - sqrt( (-1)^2 - 4 * (2)*(-14)))/(2*2)
Which is the same as x1 = ( 1 + sqrt( 1+112))/(4) and x2 = ( 1 - sqrt( 1+112))/(4)
Which make x1 = ( 1 + sqrt( 113))/(4) and x2 = ( 1 - sqrt( 113))/(4)
It imply that x1 = ( 1 + 10.6301458127346 )/(4) and x2 = ( 1 - 10.6301458127346 )/(4)
We get following answers x1 = 2.90753645318366 and x2 = -2.40753645318366

1B. Use completing the square to find the root of the equation !
2*x^2 - x - 14 = 0 ,divide both side with 2
So we get x^2 - 0.5*x - 7 = 0 ,
The coefficient of x is -0.5
We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -0.5/2 = -0.25
Next, we have to separate the constant to form x^2 - 0.5*x + 0.0625 - 7.0625 = 0
Which can be turned into ( x - 0.25 )^2 - 7.0625 = 0
Which can be turned into (( x - 0.25 ) - 2.65753645318366 ) * (( x - 0.25 ) + 2.65753645318366 ) = 0
Which is the same with ( x - 0.25 - 2.65753645318366 ) * ( x - 0.25 + 2.65753645318366 ) = 0
Just add up the constants in each brackets, and we get ( x - 2.90753645318366 ) * ( x + 2.40753645318366 ) = 0
So we have the answers x1 = 2.90753645318366 and x2 = -2.40753645318366

x=[1 + & - (1+112)^1/2]/4=2.9 & -2.4