4x(x-2)=1

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Solution for 4x(x-2)=1 equation:


Simplifying
4x(x + -2) = 1

Reorder the terms:
4x(-2 + x) = 1
(-2 * 4x + x * 4x) = 1
(-8x + 4x2) = 1

Solving
-8x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -8x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -8x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-0.25 + -2x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2x + x2 = 0 + 0.25
-2x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2x + x2 = 0.25

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.25 + 1

Reorder the terms:
1 + -2x + x2 = 0.25 + 1

Combine like terms: 0.25 + 1 = 1.25
1 + -2x + x2 = 1.25

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -1) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -1 = 1.118033989 Simplifying x + -1 = 1.118033989 Reorder the terms: -1 + x = 1.118033989 Solving -1 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.118033989 + 1 x = 1.118033989 + 1 Combine like terms: 1.118033989 + 1 = 2.118033989 x = 2.118033989 Simplifying x = 2.118033989

Subproblem 2

x + -1 = -1.118033989 Simplifying x + -1 = -1.118033989 Reorder the terms: -1 + x = -1.118033989 Solving -1 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.118033989 + 1 x = -1.118033989 + 1 Combine like terms: -1.118033989 + 1 = -0.118033989 x = -0.118033989 Simplifying x = -0.118033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.118033989, -0.118033989}

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