# (2x-1)*(4x-1)=14

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## Solution for (2x-1)*(4x-1)=14 equation:

Simplifying
(2x + -1)(4x + -1) = 14
Reorder the terms:
(-1 + 2x)(4x + -1) = 14
Reorder the terms:
(-1 + 2x)(-1 + 4x) = 14
Multiply (-1 + 2x) * (-1 + 4x)
(-1(-1 + 4x) + 2x * (-1 + 4x)) = 14
((-1 * -1 + 4x * -1) + 2x * (-1 + 4x)) = 14
((1 + -4x) + 2x * (-1 + 4x)) = 14
(1 + -4x + (-1 * 2x + 4x * 2x)) = 14
(1 + -4x + (-2x + 8x2)) = 14
Combine like terms: -4x + -2x = -6x
(1 + -6x + 8x2) = 14
Solving
1 + -6x + 8x2 = 14
Solving for variable 'x'.
Reorder the terms:
1 + -14 + -6x + 8x2 = 14 + -14
Combine like terms: 1 + -14 = -13
-13 + -6x + 8x2 = 14 + -14
Combine like terms: 14 + -14 = 0
-13 + -6x + 8x2 = 0
Begin completing the square. Divide all terms by
8 the coefficient of the squared term:
Divide each side by '8'.
-1.625 + -0.75x + x2 = 0
Move the constant term to the right:
Add '1.625' to each side of the equation.
-1.625 + -0.75x + 1.625 + x2 = 0 + 1.625
Reorder the terms:
-1.625 + 1.625 + -0.75x + x2 = 0 + 1.625
Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -0.75x + x2 = 0 + 1.625
-0.75x + x2 = 0 + 1.625
Combine like terms: 0 + 1.625 = 1.625
-0.75x + x2 = 1.625
The x term is -0.75x. Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.
Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 1.625 + 0.140625
Reorder the terms:
0.140625 + -0.75x + x2 = 1.625 + 0.140625
Combine like terms: 1.625 + 0.140625 = 1.765625
0.140625 + -0.75x + x2 = 1.765625
Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.765625
Calculate the square root of the right side: 1.328768227
Break this problem into two subproblems by setting
(x + -0.375) equal to 1.328768227 and -1.328768227.
Subproblem 1x + -0.375 = 1.328768227
Simplifying
x + -0.375 = 1.328768227
Reorder the terms:
-0.375 + x = 1.328768227
Solving
-0.375 + x = 1.328768227
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.328768227 + 0.375
Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.328768227 + 0.375
x = 1.328768227 + 0.375
Combine like terms: 1.328768227 + 0.375 = 1.703768227
x = 1.703768227
Simplifying
x = 1.703768227
Subproblem 2x + -0.375 = -1.328768227
Simplifying
x + -0.375 = -1.328768227
Reorder the terms:
-0.375 + x = -1.328768227
Solving
-0.375 + x = -1.328768227
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.328768227 + 0.375
Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.328768227 + 0.375
x = -1.328768227 + 0.375
Combine like terms: -1.328768227 + 0.375 = -0.953768227
x = -0.953768227
Simplifying
x = -0.953768227
SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {1.703768227, -0.953768227}`