4x^2-27x+6=-6+1

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Solution for 4x^2-27x+6=-6+1 equation: 


Simplifying
4x2 + -27x + 6 = -6 + 1

Reorder the terms:
6 + -27x + 4x2 = -6 + 1

Combine like terms: -6 + 1 = -5
6 + -27x + 4x2 = -5

Solving
6 + -27x + 4x2 = -5

Solving for variable 'x'.

Reorder the terms:
6 + 5 + -27x + 4x2 = -5 + 5

Combine like terms: 6 + 5 = 11
11 + -27x + 4x2 = -5 + 5

Combine like terms: -5 + 5 = 0
11 + -27x + 4x2 = 0

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

Divide each side by '4'.
2.75 + -6.75x + x2 = 0

Move the constant term to the right:

Add '-2.75' to each side of the equation.
2.75 + -6.75x + -2.75 + x2 = 0 + -2.75

Reorder the terms:
2.75 + -2.75 + -6.75x + x2 = 0 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + -6.75x + x2 = 0 + -2.75
-6.75x + x2 = 0 + -2.75

Combine like terms: 0 + -2.75 = -2.75
-6.75x + x2 = -2.75

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -2.75 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -2.75 + 11.390625

Combine like terms: -2.75 + 11.390625 = 8.640625
11.390625 + -6.75x + x2 = 8.640625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 8.640625

Calculate the square root of the right side: 2.939494004

Break this problem into two subproblems by setting 
(x + -3.375) equal to 2.939494004 and -2.939494004.


Subproblem 1
x + -3.375 = 2.939494004

Simplifying
x + -3.375 = 2.939494004

Reorder the terms:
-3.375 + x = 2.939494004

Solving
-3.375 + x = 2.939494004

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.375' to each side of the equation.
-3.375 + 3.375 + x = 2.939494004 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + x = 2.939494004 + 3.375
x = 2.939494004 + 3.375

Combine like terms: 2.939494004 + 3.375 = 6.314494004
x = 6.314494004

Simplifying
x = 6.314494004


Subproblem 2
x + -3.375 = -2.939494004

Simplifying
x + -3.375 = -2.939494004

Reorder the terms:
-3.375 + x = -2.939494004

Solving
-3.375 + x = -2.939494004

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.375' to each side of the equation.
-3.375 + 3.375 + x = -2.939494004 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + x = -2.939494004 + 3.375
x = -2.939494004 + 3.375

Combine like terms: -2.939494004 + 3.375 = 0.435505996
x = 0.435505996

Simplifying
x = 0.435505996


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.314494004, 0.435505996}

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