9647393x+1=4x(4x-1)

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Solution for 9647393x+1=4x(4x-1) equation:


Simplifying
9647393x + 1 = 4x(4x + -1)

Reorder the terms:
1 + 9647393x = 4x(4x + -1)

Reorder the terms:
1 + 9647393x = 4x(-1 + 4x)
1 + 9647393x = (-1 * 4x + 4x * 4x)
1 + 9647393x = (-4x + 16x2)

Solving
1 + 9647393x = -4x + 16x2

Solving for variable 'x'.

Combine like terms: 9647393x + 4x = 9647397x
1 + 9647397x + -16x2 = -4x + 16x2 + 4x + -16x2

Reorder the terms:
1 + 9647397x + -16x2 = -4x + 4x + 16x2 + -16x2

Combine like terms: -4x + 4x = 0
1 + 9647397x + -16x2 = 0 + 16x2 + -16x2
1 + 9647397x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
1 + 9647397x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.0625 + -602962.3125x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -602962.3125x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -602962.3125x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -602962.3125x + x2 = 0 + 0.0625
-602962.3125x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-602962.3125x + x2 = 0.0625

The x term is -602962.3125x.  Take half its coefficient (-301481.1563).
Square it (90890887600) and add it to both sides.

Add '90890887600' to each side of the equation.
-602962.3125x + 90890887600 + x2 = 0.0625 + 90890887600

Reorder the terms:
90890887600 + -602962.3125x + x2 = 0.0625 + 90890887600

Combine like terms: 0.0625 + 90890887600 = 90890887600.0625
90890887600 + -602962.3125x + x2 = 90890887600.0625

Factor a perfect square on the left side:
(x + -301481.1563)(x + -301481.1563) = 90890887600.0625

Calculate the square root of the right side: 301481.156293495

Break this problem into two subproblems by setting 
(x + -301481.1563) equal to 301481.156293495 and -301481.156293495.

Subproblem 1

x + -301481.1563 = 301481.156293495 Simplifying x + -301481.1563 = 301481.156293495 Reorder the terms: -301481.1563 + x = 301481.156293495 Solving -301481.1563 + x = 301481.156293495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '301481.1563' to each side of the equation. -301481.1563 + 301481.1563 + x = 301481.156293495 + 301481.1563 Combine like terms: -301481.1563 + 301481.1563 = 0.0000 0.0000 + x = 301481.156293495 + 301481.1563 x = 301481.156293495 + 301481.1563 Combine like terms: 301481.156293495 + 301481.1563 = 602962.312593495 x = 602962.312593495 Simplifying x = 602962.312593495

Subproblem 2

x + -301481.1563 = -301481.156293495 Simplifying x + -301481.1563 = -301481.156293495 Reorder the terms: -301481.1563 + x = -301481.156293495 Solving -301481.1563 + x = -301481.156293495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '301481.1563' to each side of the equation. -301481.1563 + 301481.1563 + x = -301481.156293495 + 301481.1563 Combine like terms: -301481.1563 + 301481.1563 = 0.0000 0.0000 + x = -301481.156293495 + 301481.1563 x = -301481.156293495 + 301481.1563 Combine like terms: -301481.156293495 + 301481.1563 = 0.000006505 x = 0.000006505 Simplifying x = 0.000006505

Solution

The solution to the problem is based on the solutions from the subproblems. x = {602962.312593495, 0.000006505}

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