Question

Please help me! Solve this quadratic equation using the quadratic formula.

2x^2 - 2x = 1

Answer 1

`(-(-2)+- √((-2)^2-4*2*(-1)) )/(2*2) = (2+- √(12) )/(4)`

`x1= (2+ √(12) )/(4)= 1,37`

`x2= (2- √(12) )/(4)= -0,37`

Answer 2

for 0=ax²+bx+c

quadratic formula can be used to solve for x like this

`x= (-b+/- √(b^2-4ac) )/(2a)`
given
2x²-2x=1
minus 1 both sides
2x²-2x-1=0
a=1
b=-2
c=-1




`x= (-(-2)+/- √((-2)^2-4(2)(-1)) )/(2(2))`

`x= (2+/- √(4+8) )/(4)`

`x= (2+/- √(12) )/(4)`

`x= (2+/- (√(4))(√(3)) )/(4)`

`x= (2+/- (2)(√(3)) )/(4)`

`x= (2+/- 2√(3) )/(4)`

`x= (1+/- √(3) )/(2)`


`x= (1+ √(3) )/(2)` or
`x= (1- √(3) )/(2)`