3x^2-42x+78=0

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Solution for 3x^2-42x+78=0 equation: 


Simplifying
3x2 + -42x + 78 = 0

Reorder the terms:
78 + -42x + 3x2 = 0

Solving
78 + -42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(26 + -14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(26 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
26 + -14x + x2 = 0

Solving
26 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -14x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + -14x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -14x + x2 = 0 + -26
-14x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
-14x + x2 = -26

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -26 + 49

Reorder the terms:
49 + -14x + x2 = -26 + 49

Combine like terms: -26 + 49 = 23
49 + -14x + x2 = 23

Factor a perfect square on the left side:
(x + -7)(x + -7) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + -7) equal to 4.795831523 and -4.795831523.


Subproblem 1
x + -7 = 4.795831523

Simplifying
x + -7 = 4.795831523

Reorder the terms:
-7 + x = 4.795831523

Solving
-7 + x = 4.795831523

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 4.795831523 + 7

Combine like terms: -7 + 7 = 0
0 + x = 4.795831523 + 7
x = 4.795831523 + 7

Combine like terms: 4.795831523 + 7 = 11.795831523
x = 11.795831523

Simplifying
x = 11.795831523


Subproblem 2
x + -7 = -4.795831523

Simplifying
x + -7 = -4.795831523

Reorder the terms:
-7 + x = -4.795831523

Solving
-7 + x = -4.795831523

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -4.795831523 + 7

Combine like terms: -7 + 7 = 0
0 + x = -4.795831523 + 7
x = -4.795831523 + 7

Combine like terms: -4.795831523 + 7 = 2.204168477
x = 2.204168477

Simplifying
x = 2.204168477


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.795831523, 2.204168477}
Solution
x = {11.795831523, 2.204168477}

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