Question 392503: 4x2 - 4x + 3 = 0
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! ~= square root and \= +-
4x^(2)-4x+3=0
Use the quadratic formula to find the solutions. In this case, the values are a=4, b=-4, and c=3.
x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0
Use the standard form of the equation to find a, b, and c for this quadratic.
a=4, b=-4, and c=3
Substitute in the values of a=4, b=-4, and c=3.
x=(-(-4)\~((-4)^(2)-4(4)(3)))/(2(4))
Multiply -1 by each term inside the parentheses.
x=(4\~((-4)^(2)-4(4)(3)))/(2(4))
Simplify the section inside the radical.
x=(4\4i~(2))/(2(4))
Simplify the denominator of the quadratic formula.
x=(4\4i~(2))/(8)
First, solve the + portion of \.
x=(4+4i~(2))/(8)
Simplify the expression to solve for the + portion of the \.
x=(1+i~(2))/(2)
Next, solve the - portion of \.
x=(4-4i~(2))/(8)
Simplify the expression to solve for the - portion of the \.
x=(1-i~(2))/(2)
The final answer is the combination of both solutions.
x=(1+i~(2))/(2),(1-i~(2))/(2)
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