3x^2-14x=26

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Solution for 3x^2-14x=26 equation: 


Simplifying
3x2 + -14x = 26

Reorder the terms:
-14x + 3x2 = 26

Solving
-14x + 3x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + -14x + 3x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + -14x + 3x2 = 0

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

Divide each side by '3'.
-8.666666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '8.666666667' to each side of the equation.
-8.666666667 + -4.666666667x + 8.666666667 + x2 = 0 + 8.666666667

Reorder the terms:
-8.666666667 + 8.666666667 + -4.666666667x + x2 = 0 + 8.666666667

Combine like terms: -8.666666667 + 8.666666667 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 8.666666667
-4.666666667x + x2 = 0 + 8.666666667

Combine like terms: 0 + 8.666666667 = 8.666666667
-4.666666667x + x2 = 8.666666667

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 8.666666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 8.666666667 + 5.444444448

Combine like terms: 8.666666667 + 5.444444448 = 14.111111115
5.444444448 + -4.666666667x + x2 = 14.111111115

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 14.111111115

Calculate the square root of the right side: 3.75647589

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 3.75647589 and -3.75647589.


Subproblem 1
x + -2.333333334 = 3.75647589

Simplifying
x + -2.333333334 = 3.75647589

Reorder the terms:
-2.333333334 + x = 3.75647589

Solving
-2.333333334 + x = 3.75647589

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 3.75647589 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 3.75647589 + 2.333333334
x = 3.75647589 + 2.333333334

Combine like terms: 3.75647589 + 2.333333334 = 6.089809224
x = 6.089809224

Simplifying
x = 6.089809224


Subproblem 2
x + -2.333333334 = -3.75647589

Simplifying
x + -2.333333334 = -3.75647589

Reorder the terms:
-2.333333334 + x = -3.75647589

Solving
-2.333333334 + x = -3.75647589

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -3.75647589 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -3.75647589 + 2.333333334
x = -3.75647589 + 2.333333334

Combine like terms: -3.75647589 + 2.333333334 = -1.423142556
x = -1.423142556

Simplifying
x = -1.423142556


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.089809224, -1.423142556}

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