SOLUTION: 1/4=3-2x-1/x+2

Question 345958: 1/4=3-2x-1/x+2
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
(1)/(4)=3-2x-(1)/(x)+2 All / signs stand for +- and all ~ signs stand for the square root.
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.
3-2x-(1)/(x)+2=(1)/(4)
Add 2 to 3 to get 5.
5-2x-(1)/(x)=(1)/(4)
Find the LCD (least common denominator) of -2x+5-(1)/(x)+(1)/(4).
Least common denominator: 4x
Multiply each term in the equation by 4x in order to remove all the denominators from the equation.
-2x*4x+5*4x-(1)/(x)*4x=(1)/(4)*4x
Simplify the left-hand side of the equation by canceling the common factors.
-8x^(2)+20x-4=(1)/(4)*4x
Simplify the right-hand side of the equation by simplifying each term.
-8x^(2)+20x-4=x
Since x contains the variable to solve for, move it to the left-hand side of the equation by subtracting x from both sides.
-8x^(2)+20x-4-x=0
Since 20x and -x are like terms, add -x to 20x to get 19x.
-8x^(2)+19x-4=0
Multiply each term in the equation by -1.
-8x^(2)*-1+19x*-1-4*-1=0*-1
Simplify the left-hand side of the equation by multiplying out all the terms.
8x^(2)-19x+4=0*-1
Multiply 0 by -1 to get 0.
8x^(2)-19x+4=0
Use the quadratic formula to find the solutions. In this case, the values are a=8, b=-19, and c=4.
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=8, b=-19, and c=4
Substitute in the values of a=8, b=-19, and c=4.
x=(-(-19)\~((-19)^(2)-4(8)(4)))/(2(8))
Multiply -1 by each term inside the parentheses.
x=(19\~((-19)^(2)-4(8)(4)))/(2(8))
Simplify the section inside the radical.
x=(19\~(233))/(2(8))
Simplify the denominator of the quadratic formula.
x=(19\~(233))/(16)
First, solve the + portion of \.
x=(19+~(233))/(16)
Next, solve the - portion of \.
x=(19-~(233))/(16)
The final answer is the combination of both solutions.
x=(19+~(233))/(16),(19-~(233))/(16)_x=2.14,0.23
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