6x*6x+3-7x-4x-4x-11x=

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Solution for 6x*6x+3-7x-4x-4x-11x= equation:


Simplifying
6x * 6x + 3 + -7x + -4x + -4x + -11x = 0

Reorder the terms for easier multiplication:
6 * 6x * x + 3 + -7x + -4x + -4x + -11x = 0

Multiply 6 * 6
36x * x + 3 + -7x + -4x + -4x + -11x = 0

Multiply x * x
36x2 + 3 + -7x + -4x + -4x + -11x = 0

Reorder the terms:
3 + -7x + -4x + -4x + -11x + 36x2 = 0

Combine like terms: -7x + -4x = -11x
3 + -11x + -4x + -11x + 36x2 = 0

Combine like terms: -11x + -4x = -15x
3 + -15x + -11x + 36x2 = 0

Combine like terms: -15x + -11x = -26x
3 + -26x + 36x2 = 0

Solving
3 + -26x + 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'.
0.08333333333 + -0.7222222222x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + -0.7222222222x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + -0.7222222222x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + -0.7222222222x + x2 = 0 + -0.08333333333
-0.7222222222x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
-0.7222222222x + x2 = -0.08333333333

The x term is -0.7222222222x.  Take half its coefficient (-0.3611111111).
Square it (0.1304012346) and add it to both sides.

Add '0.1304012346' to each side of the equation.
-0.7222222222x + 0.1304012346 + x2 = -0.08333333333 + 0.1304012346

Reorder the terms:
0.1304012346 + -0.7222222222x + x2 = -0.08333333333 + 0.1304012346

Combine like terms: -0.08333333333 + 0.1304012346 = 0.04706790127
0.1304012346 + -0.7222222222x + x2 = 0.04706790127

Factor a perfect square on the left side:
(x + -0.3611111111)(x + -0.3611111111) = 0.04706790127

Calculate the square root of the right side: 0.21695138

Break this problem into two subproblems by setting 
(x + -0.3611111111) equal to 0.21695138 and -0.21695138.

Subproblem 1

x + -0.3611111111 = 0.21695138 Simplifying x + -0.3611111111 = 0.21695138 Reorder the terms: -0.3611111111 + x = 0.21695138 Solving -0.3611111111 + x = 0.21695138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3611111111' to each side of the equation. -0.3611111111 + 0.3611111111 + x = 0.21695138 + 0.3611111111 Combine like terms: -0.3611111111 + 0.3611111111 = 0.0000000000 0.0000000000 + x = 0.21695138 + 0.3611111111 x = 0.21695138 + 0.3611111111 Combine like terms: 0.21695138 + 0.3611111111 = 0.5780624911 x = 0.5780624911 Simplifying x = 0.5780624911

Subproblem 2

x + -0.3611111111 = -0.21695138 Simplifying x + -0.3611111111 = -0.21695138 Reorder the terms: -0.3611111111 + x = -0.21695138 Solving -0.3611111111 + x = -0.21695138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3611111111' to each side of the equation. -0.3611111111 + 0.3611111111 + x = -0.21695138 + 0.3611111111 Combine like terms: -0.3611111111 + 0.3611111111 = 0.0000000000 0.0000000000 + x = -0.21695138 + 0.3611111111 x = -0.21695138 + 0.3611111111 Combine like terms: -0.21695138 + 0.3611111111 = 0.1441597311 x = 0.1441597311 Simplifying x = 0.1441597311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5780624911, 0.1441597311}

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