What is the quadratic equation for 2x2+x-1=0? I am having trouble with the middle x.?

x = [-b ± √(b² - 4ac)] / 2a

a = 2, b = 1. c = -1

x = [ -1 ± √( (1)² - (4)(2)(-1) ) ] / (2)(2)

x = [ -1 ± √ ( 1 - (-8)) ] / 4

x = [ -1 ± √9 ] / 4

x = ( - 1 ± 3 ) / 4

x = (-1 + 3) / 4 = 2/4 = 1/2, or (-1 - 3) / 4 = -4/4 = -1

Axis of symmetry is x = -b/2a, so x = -a million/4 The vertex lies on the axis of symmetry so plug x = -a million/4 into y=-2x^2-x+3 getting y = -a million/8 +a million/4 + 3 =3 a million/8 = 25/8. So vertex is (-a million/4, 25/8). x-intercepts are a million and - 3/2 utilizing quadratic formula. Set x = 0 and get y = 3 ,so (0,3) is y-intercept.

Question Number 1 :
For this equation 2*x^2 + x - 1 = 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 - 1 = 0 is already in a*x^2+b*x+c=0 form.
By matching the constant position, we can derive that the value of a = 2, b = 1, c = -1.

1A. Find the roots using Quadratic Formula !
By using abc formula the value of x is both
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
As a = 2, b = 1 and c = -1,
then the value a,b and c in the abc formula, can be subtituted.
So x1 = (-(1) + sqrt( (1)^2 - 4 * (2)*(-1)))/(2*2) and x2 = (-(1) - sqrt( (1)^2 - 4 * (2)*(-1)))/(2*2)
Which is the same as x1 = ( -1 + sqrt( 1+8))/(4) and x2 = ( -1 - sqrt( 1+8))/(4)
Which is the same as x1 = ( -1 + sqrt( 9))/(4) and x2 = ( -1 - sqrt( 9))/(4)
We can get x1 = ( -1 + 3 )/(4) and x2 = ( -1 - 3 )/(4)
We get following answers x1 = 0.5 and x2 = -1

1B. Use completing the square to find the root of the equation !
2*x^2 + x - 1 = 0 ,divide both side with 2
By doing so we get x^2 + 0.5*x - 0.5 = 0 ,
And 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
So we have make the equation into x^2 + 0.5*x + 0.0625 - 0.5625 = 0
Which is the same with ( x + 0.25 )^2 - 0.5625 = 0
Which can be turned into (( x + 0.25 ) - 0.75 ) * (( x + 0.25 ) + 0.75 ) = 0
And it is the same with ( x + 0.25 - 0.75 ) * ( x + 0.25 + 0.75 ) = 0
Just add up the constants in each brackets, and we get ( x - 0.5 ) * ( x + 1 ) = 0
So we got the answers as x1 = 0.5 and x2 = -1

This IS a quadratic equation !!!

x = [ - 1 ± √ (1 + 8) ] / 4
x = [ - 1 ± 3 ] / 4
x = 1/2 , x = - 1
OR
(2x - 1)(x + 1) = 0
x = 1/2 , x = - 1

2x2+x-1=0
4+x-1=0
move all the numbers to the right (positive becomes negative and vice versa)
x=0-4+1=-3

The general form of quadratic equations is
a x^2 + b x + c = 0 . . . . . . (a different from 0)

In this case:
2 x^2 + 1 x + (-1) = 0

a = 2, b = 1, c = -1

2x^2+x-1=0
2x^2 + 2x - 1x - 1 = 0
2x(x + 1) - 1(x + 1) = 0
(2x - 1)(x + 1) = 0
x = 1/2 or -1

Assuming that means 2 * (x^2) + x - 1 =0, that is the quadratic equation.

When factored it becomes (2x - 1) * (x + 1) = 0, so the solutions are

1/2 and -1

2x^2 + x - 1 = 0
2x^2 + 2x - x - 1 = 0
(2x^2 + 2x) - (x + 1) = 0
2x(x + 1) - 1(x + 1) = 0
(x + 1)(2x - 1) = 0

x + 1 = 0
x = -1

2x - 1 = 0
2x = 1
x = 1/2 (0.5)

∴ x = -1 , 1/2 (0.5)

it would be -1 plus/minus the square root of [1^2 - (4*2*-1)] all over 2*2