SOLUTION: I previously asked this question but it came out wrong and when it was answered I saw how I had grouped it incorrectly. Trying again. ((sq. rt.5)-1)/x = ((sq.rt.5)/2)

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Question 430065: I previously asked this question but it came out wrong and when it was answered I saw how I had grouped it incorrectly. Trying again.
((sq. rt.5)-1)/x = ((sq.rt.5)/2)
Answer by haileytucki(390) (Show Source):
You can put this solution on YOUR website!
NOTE: ~ is symbol for square root
((~(0.5))-1)/(x)=((~(0.5))/(2))
Take the square root of 0.5 to get 0.7071067812.
((0.7071067812)-1)/(x)=((~(0.5))/(2))
Remove the parentheses around the expression 0.7071067812.
(0.7071067812-1)/(x)=((~(0.5))/(2))
Subtract 1 from 0.7071067812 to get -0.2928932.
(-0.2928932)/(x)=((~(0.5))/(2))
Move the minus sign from the numerator to the front of the expression.
-(0.2928932)/(x)=((~(0.5))/(2))
Check that all solutions found are valid and are part of the domain by substituting them into the original equation.
x=((~(0.5))/(2))
Multiply each term in the equation by x.
-(0.2928932)/(x)*x=((~(0.5))/(2))*x
Simplify the left-hand side of the equation by canceling the common factors.
-0.2928932=((~(0.5))/(2))*x
Simplify the right-hand side of the equation by multiplying out all the terms.
-0.2928932=0.3535533906x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
0.3535533906x=-0.2928932
Divide each term in the equation by 0.3535533906.
(0.3535533906x)/(0.3535533906)=-(0.2928932)/(0.3535533906)
Cancel the common factor of 0.3535533906.
x=-(0.2928932)/(0.3535533906)
Divide -0.2928932 by 0.3535533906 to get -0.8284270715.
x=-0.8284270715