14x^2-135x+40=0

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Solution for 14x^2-135x+40=0 equation: 


Simplifying
14x2 + -135x + 40 = 0

Reorder the terms:
40 + -135x + 14x2 = 0

Solving
40 + -135x + 14x2 = 0

Solving for variable 'x'.

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

Divide each side by '14'.
2.857142857 + -9.642857143x + x2 = 0

Move the constant term to the right:

Add '-2.857142857' to each side of the equation.
2.857142857 + -9.642857143x + -2.857142857 + x2 = 0 + -2.857142857

Reorder the terms:
2.857142857 + -2.857142857 + -9.642857143x + x2 = 0 + -2.857142857

Combine like terms: 2.857142857 + -2.857142857 = 0.000000000
0.000000000 + -9.642857143x + x2 = 0 + -2.857142857
-9.642857143x + x2 = 0 + -2.857142857

Combine like terms: 0 + -2.857142857 = -2.857142857
-9.642857143x + x2 = -2.857142857

The x term is -9.642857143x.  Take half its coefficient (-4.821428572).
Square it (23.24617347) and add it to both sides.

Add '23.24617347' to each side of the equation.
-9.642857143x + 23.24617347 + x2 = -2.857142857 + 23.24617347

Reorder the terms:
23.24617347 + -9.642857143x + x2 = -2.857142857 + 23.24617347

Combine like terms: -2.857142857 + 23.24617347 = 20.389030613
23.24617347 + -9.642857143x + x2 = 20.389030613

Factor a perfect square on the left side:
(x + -4.821428572)(x + -4.821428572) = 20.389030613

Calculate the square root of the right side: 4.515421421

Break this problem into two subproblems by setting 
(x + -4.821428572) equal to 4.515421421 and -4.515421421.


Subproblem 1
x + -4.821428572 = 4.515421421

Simplifying
x + -4.821428572 = 4.515421421

Reorder the terms:
-4.821428572 + x = 4.515421421

Solving
-4.821428572 + x = 4.515421421

Solving for variable 'x'.

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

Add '4.821428572' to each side of the equation.
-4.821428572 + 4.821428572 + x = 4.515421421 + 4.821428572

Combine like terms: -4.821428572 + 4.821428572 = 0.000000000
0.000000000 + x = 4.515421421 + 4.821428572
x = 4.515421421 + 4.821428572

Combine like terms: 4.515421421 + 4.821428572 = 9.336849993
x = 9.336849993

Simplifying
x = 9.336849993


Subproblem 2
x + -4.821428572 = -4.515421421

Simplifying
x + -4.821428572 = -4.515421421

Reorder the terms:
-4.821428572 + x = -4.515421421

Solving
-4.821428572 + x = -4.515421421

Solving for variable 'x'.

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

Add '4.821428572' to each side of the equation.
-4.821428572 + 4.821428572 + x = -4.515421421 + 4.821428572

Combine like terms: -4.821428572 + 4.821428572 = 0.000000000
0.000000000 + x = -4.515421421 + 4.821428572
x = -4.515421421 + 4.821428572

Combine like terms: -4.515421421 + 4.821428572 = 0.306007151
x = 0.306007151

Simplifying
x = 0.306007151


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.336849993, 0.306007151}

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