91=3x(x-14)

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Solution for 91=3x(x-14) equation: 


Simplifying
91 = 3x(x + -14)

Reorder the terms:
91 = 3x(-14 + x)
91 = (-14 * 3x + x * 3x)
91 = (-42x + 3x2)

Solving
91 = -42x + 3x2

Solving for variable 'x'.

Reorder the terms:
91 + 42x + -3x2 = -42x + 42x + 3x2 + -3x2

Combine like terms: -42x + 42x = 0
91 + 42x + -3x2 = 0 + 3x2 + -3x2
91 + 42x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
91 + 42x + -3x2 = 0

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

Divide each side by '-3'.
-30.33333333 + -14x + x2 = 0

Move the constant term to the right:

Add '30.33333333' to each side of the equation.
-30.33333333 + -14x + 30.33333333 + x2 = 0 + 30.33333333

Reorder the terms:
-30.33333333 + 30.33333333 + -14x + x2 = 0 + 30.33333333

Combine like terms: -30.33333333 + 30.33333333 = 0.00000000
0.00000000 + -14x + x2 = 0 + 30.33333333
-14x + x2 = 0 + 30.33333333

Combine like terms: 0 + 30.33333333 = 30.33333333
-14x + x2 = 30.33333333

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 = 30.33333333 + 49

Reorder the terms:
49 + -14x + x2 = 30.33333333 + 49

Combine like terms: 30.33333333 + 49 = 79.33333333
49 + -14x + x2 = 79.33333333

Factor a perfect square on the left side:
(x + -7)(x + -7) = 79.33333333

Calculate the square root of the right side: 8.906926144

Break this problem into two subproblems by setting 
(x + -7) equal to 8.906926144 and -8.906926144.


Subproblem 1
x + -7 = 8.906926144

Simplifying
x + -7 = 8.906926144

Reorder the terms:
-7 + x = 8.906926144

Solving
-7 + x = 8.906926144

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 = 8.906926144 + 7

Combine like terms: -7 + 7 = 0
0 + x = 8.906926144 + 7
x = 8.906926144 + 7

Combine like terms: 8.906926144 + 7 = 15.906926144
x = 15.906926144

Simplifying
x = 15.906926144


Subproblem 2
x + -7 = -8.906926144

Simplifying
x + -7 = -8.906926144

Reorder the terms:
-7 + x = -8.906926144

Solving
-7 + x = -8.906926144

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 = -8.906926144 + 7

Combine like terms: -7 + 7 = 0
0 + x = -8.906926144 + 7
x = -8.906926144 + 7

Combine like terms: -8.906926144 + 7 = -1.906926144
x = -1.906926144

Simplifying
x = -1.906926144


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.906926144, -1.906926144}

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