(x^2-9x+20)+(x^2-6x+5)+(x^2-5x+4)=

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Solution for (x^2-9x+20)+(x^2-6x+5)+(x^2-5x+4)= equation: 


Simplifying
(x2 + -9x + 20) + (x2 + -6x + 5) + (x2 + -5x + 4) = 0

Reorder the terms:
(20 + -9x + x2) + (x2 + -6x + 5) + (x2 + -5x + 4) = 0

Remove parenthesis around (20 + -9x + x2)
20 + -9x + x2 + (x2 + -6x + 5) + (x2 + -5x + 4) = 0

Reorder the terms:
20 + -9x + x2 + (5 + -6x + x2) + (x2 + -5x + 4) = 0

Remove parenthesis around (5 + -6x + x2)
20 + -9x + x2 + 5 + -6x + x2 + (x2 + -5x + 4) = 0

Reorder the terms:
20 + -9x + x2 + 5 + -6x + x2 + (4 + -5x + x2) = 0

Remove parenthesis around (4 + -5x + x2)
20 + -9x + x2 + 5 + -6x + x2 + 4 + -5x + x2 = 0

Reorder the terms:
20 + 5 + 4 + -9x + -6x + -5x + x2 + x2 + x2 = 0

Combine like terms: 20 + 5 = 25
25 + 4 + -9x + -6x + -5x + x2 + x2 + x2 = 0

Combine like terms: 25 + 4 = 29
29 + -9x + -6x + -5x + x2 + x2 + x2 = 0

Combine like terms: -9x + -6x = -15x
29 + -15x + -5x + x2 + x2 + x2 = 0

Combine like terms: -15x + -5x = -20x
29 + -20x + x2 + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
29 + -20x + 2x2 + x2 = 0

Combine like terms: 2x2 + x2 = 3x2
29 + -20x + 3x2 = 0

Solving
29 + -20x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
9.666666667 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-9.666666667' to each side of the equation.
9.666666667 + -6.666666667x + -9.666666667 + x2 = 0 + -9.666666667

Reorder the terms:
9.666666667 + -9.666666667 + -6.666666667x + x2 = 0 + -9.666666667

Combine like terms: 9.666666667 + -9.666666667 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -9.666666667
-6.666666667x + x2 = 0 + -9.666666667

Combine like terms: 0 + -9.666666667 = -9.666666667
-6.666666667x + x2 = -9.666666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -9.666666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -9.666666667 + 11.11111112

Combine like terms: -9.666666667 + 11.11111112 = 1.444444453
11.11111112 + -6.666666667x + x2 = 1.444444453

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 1.444444453

Calculate the square root of the right side: 1.201850429

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 1.201850429 and -1.201850429.


Subproblem 1
x + -3.333333334 = 1.201850429

Simplifying
x + -3.333333334 = 1.201850429

Reorder the terms:
-3.333333334 + x = 1.201850429

Solving
-3.333333334 + x = 1.201850429

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 1.201850429 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 1.201850429 + 3.333333334
x = 1.201850429 + 3.333333334

Combine like terms: 1.201850429 + 3.333333334 = 4.535183763
x = 4.535183763

Simplifying
x = 4.535183763


Subproblem 2
x + -3.333333334 = -1.201850429

Simplifying
x + -3.333333334 = -1.201850429

Reorder the terms:
-3.333333334 + x = -1.201850429

Solving
-3.333333334 + x = -1.201850429

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -1.201850429 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -1.201850429 + 3.333333334
x = -1.201850429 + 3.333333334

Combine like terms: -1.201850429 + 3.333333334 = 2.131482905
x = 2.131482905

Simplifying
x = 2.131482905


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.535183763, 2.131482905}

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