(6x+1)-4x(9x+2)=

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Solution for (6x+1)-4x(9x+2)= equation:


Simplifying
(6x + 1) + -4x(9x + 2) = 0

Reorder the terms:
(1 + 6x) + -4x(9x + 2) = 0

Remove parenthesis around (1 + 6x)
1 + 6x + -4x(9x + 2) = 0

Reorder the terms:
1 + 6x + -4x(2 + 9x) = 0
1 + 6x + (2 * -4x + 9x * -4x) = 0
1 + 6x + (-8x + -36x2) = 0

Combine like terms: 6x + -8x = -2x
1 + -2x + -36x2 = 0

Solving
1 + -2x + -36x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-36 the coefficient of the squared term: 

Divide each side by '-36'.
-0.02777777778 + 0.05555555556x + x2 = 0

Move the constant term to the right:

Add '0.02777777778' to each side of the equation.
-0.02777777778 + 0.05555555556x + 0.02777777778 + x2 = 0 + 0.02777777778

Reorder the terms:
-0.02777777778 + 0.02777777778 + 0.05555555556x + x2 = 0 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + 0.05555555556x + x2 = 0 + 0.02777777778
0.05555555556x + x2 = 0 + 0.02777777778

Combine like terms: 0 + 0.02777777778 = 0.02777777778
0.05555555556x + x2 = 0.02777777778

The x term is 0.05555555556x.  Take half its coefficient (0.02777777778).
Square it (0.0007716049384) and add it to both sides.

Add '0.0007716049384' to each side of the equation.
0.05555555556x + 0.0007716049384 + x2 = 0.02777777778 + 0.0007716049384

Reorder the terms:
0.0007716049384 + 0.05555555556x + x2 = 0.02777777778 + 0.0007716049384

Combine like terms: 0.02777777778 + 0.0007716049384 = 0.0285493827184
0.0007716049384 + 0.05555555556x + x2 = 0.0285493827184

Factor a perfect square on the left side:
(x + 0.02777777778)(x + 0.02777777778) = 0.0285493827184

Calculate the square root of the right side: 0.168965626

Break this problem into two subproblems by setting 
(x + 0.02777777778) equal to 0.168965626 and -0.168965626.

Subproblem 1

x + 0.02777777778 = 0.168965626 Simplifying x + 0.02777777778 = 0.168965626 Reorder the terms: 0.02777777778 + x = 0.168965626 Solving 0.02777777778 + x = 0.168965626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = 0.168965626 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = 0.168965626 + -0.02777777778 x = 0.168965626 + -0.02777777778 Combine like terms: 0.168965626 + -0.02777777778 = 0.14118784822 x = 0.14118784822 Simplifying x = 0.14118784822

Subproblem 2

x + 0.02777777778 = -0.168965626 Simplifying x + 0.02777777778 = -0.168965626 Reorder the terms: 0.02777777778 + x = -0.168965626 Solving 0.02777777778 + x = -0.168965626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = -0.168965626 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = -0.168965626 + -0.02777777778 x = -0.168965626 + -0.02777777778 Combine like terms: -0.168965626 + -0.02777777778 = -0.19674340378 x = -0.19674340378 Simplifying x = -0.19674340378

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.14118784822, -0.19674340378}

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