9x^2-68x+36=0

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Solution for 9x^2-68x+36=0 equation:


Simplifying
9x2 + -68x + 36 = 0

Reorder the terms:
36 + -68x + 9x2 = 0

Solving
36 + -68x + 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'.
4 + -7.555555556x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7.555555556x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -7.555555556x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7.555555556x + x2 = 0 + -4
-7.555555556x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-7.555555556x + x2 = -4

The x term is -7.555555556x.  Take half its coefficient (-3.777777778).
Square it (14.27160494) and add it to both sides.

Add '14.27160494' to each side of the equation.
-7.555555556x + 14.27160494 + x2 = -4 + 14.27160494

Reorder the terms:
14.27160494 + -7.555555556x + x2 = -4 + 14.27160494

Combine like terms: -4 + 14.27160494 = 10.27160494
14.27160494 + -7.555555556x + x2 = 10.27160494

Factor a perfect square on the left side:
(x + -3.777777778)(x + -3.777777778) = 10.27160494

Calculate the square root of the right side: 3.204934467

Break this problem into two subproblems by setting 
(x + -3.777777778) equal to 3.204934467 and -3.204934467.

Subproblem 1

x + -3.777777778 = 3.204934467 Simplifying x + -3.777777778 = 3.204934467 Reorder the terms: -3.777777778 + x = 3.204934467 Solving -3.777777778 + x = 3.204934467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.777777778' to each side of the equation. -3.777777778 + 3.777777778 + x = 3.204934467 + 3.777777778 Combine like terms: -3.777777778 + 3.777777778 = 0.000000000 0.000000000 + x = 3.204934467 + 3.777777778 x = 3.204934467 + 3.777777778 Combine like terms: 3.204934467 + 3.777777778 = 6.982712245 x = 6.982712245 Simplifying x = 6.982712245

Subproblem 2

x + -3.777777778 = -3.204934467 Simplifying x + -3.777777778 = -3.204934467 Reorder the terms: -3.777777778 + x = -3.204934467 Solving -3.777777778 + x = -3.204934467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.777777778' to each side of the equation. -3.777777778 + 3.777777778 + x = -3.204934467 + 3.777777778 Combine like terms: -3.777777778 + 3.777777778 = 0.000000000 0.000000000 + x = -3.204934467 + 3.777777778 x = -3.204934467 + 3.777777778 Combine like terms: -3.204934467 + 3.777777778 = 0.572843311 x = 0.572843311 Simplifying x = 0.572843311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.982712245, 0.572843311}

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