9x^2-140x+528=0

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Solution for 9x^2-140x+528=0 equation: 


Simplifying
9x2 + -140x + 528 = 0

Reorder the terms:
528 + -140x + 9x2 = 0

Solving
528 + -140x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
58.66666667 + -15.55555556x + x2 = 0

Move the constant term to the right:

Add '-58.66666667' to each side of the equation.
58.66666667 + -15.55555556x + -58.66666667 + x2 = 0 + -58.66666667

Reorder the terms:
58.66666667 + -58.66666667 + -15.55555556x + x2 = 0 + -58.66666667

Combine like terms: 58.66666667 + -58.66666667 = 0.00000000
0.00000000 + -15.55555556x + x2 = 0 + -58.66666667
-15.55555556x + x2 = 0 + -58.66666667

Combine like terms: 0 + -58.66666667 = -58.66666667
-15.55555556x + x2 = -58.66666667

The x term is -15.55555556x.  Take half its coefficient (-7.77777778).
Square it (60.49382720) and add it to both sides.

Add '60.49382720' to each side of the equation.
-15.55555556x + 60.49382720 + x2 = -58.66666667 + 60.49382720

Reorder the terms:
60.49382720 + -15.55555556x + x2 = -58.66666667 + 60.49382720

Combine like terms: -58.66666667 + 60.49382720 = 1.82716053
60.49382720 + -15.55555556x + x2 = 1.82716053

Factor a perfect square on the left side:
(x + -7.77777778)(x + -7.77777778) = 1.82716053

Calculate the square root of the right side: 1.35172502

Break this problem into two subproblems by setting 
(x + -7.77777778) equal to 1.35172502 and -1.35172502.


Subproblem 1
x + -7.77777778 = 1.35172502

Simplifying
x + -7.77777778 = 1.35172502

Reorder the terms:
-7.77777778 + x = 1.35172502

Solving
-7.77777778 + x = 1.35172502

Solving for variable 'x'.

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

Add '7.77777778' to each side of the equation.
-7.77777778 + 7.77777778 + x = 1.35172502 + 7.77777778

Combine like terms: -7.77777778 + 7.77777778 = 0.00000000
0.00000000 + x = 1.35172502 + 7.77777778
x = 1.35172502 + 7.77777778

Combine like terms: 1.35172502 + 7.77777778 = 9.1295028
x = 9.1295028

Simplifying
x = 9.1295028


Subproblem 2
x + -7.77777778 = -1.35172502

Simplifying
x + -7.77777778 = -1.35172502

Reorder the terms:
-7.77777778 + x = -1.35172502

Solving
-7.77777778 + x = -1.35172502

Solving for variable 'x'.

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

Add '7.77777778' to each side of the equation.
-7.77777778 + 7.77777778 + x = -1.35172502 + 7.77777778

Combine like terms: -7.77777778 + 7.77777778 = 0.00000000
0.00000000 + x = -1.35172502 + 7.77777778
x = -1.35172502 + 7.77777778

Combine like terms: -1.35172502 + 7.77777778 = 6.42605276
x = 6.42605276

Simplifying
x = 6.42605276


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.1295028, 6.42605276}

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