2x(4x-1)=9

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Solution for 2x(4x-1)=9 equation:


Simplifying
2x(4x + -1) = 9

Reorder the terms:
2x(-1 + 4x) = 9
(-1 * 2x + 4x * 2x) = 9
(-2x + 8x2) = 9

Solving
-2x + 8x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + -2x + 8x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -2x + 8x2 = 0

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

Divide each side by '8'.
-1.125 + -0.25x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.25x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.25x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.25x + x2 = 0 + 1.125
-0.25x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.25x + x2 = 1.125

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 1.125 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 1.125 + 0.015625

Combine like terms: 1.125 + 0.015625 = 1.140625
0.015625 + -0.25x + x2 = 1.140625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.068000468 and -1.068000468.

Subproblem 1

x + -0.125 = 1.068000468 Simplifying x + -0.125 = 1.068000468 Reorder the terms: -0.125 + x = 1.068000468 Solving -0.125 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.068000468 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.068000468 + 0.125 x = 1.068000468 + 0.125 Combine like terms: 1.068000468 + 0.125 = 1.193000468 x = 1.193000468 Simplifying x = 1.193000468

Subproblem 2

x + -0.125 = -1.068000468 Simplifying x + -0.125 = -1.068000468 Reorder the terms: -0.125 + x = -1.068000468 Solving -0.125 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.068000468 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.068000468 + 0.125 x = -1.068000468 + 0.125 Combine like terms: -1.068000468 + 0.125 = -0.943000468 x = -0.943000468 Simplifying x = -0.943000468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.193000468, -0.943000468}

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