9x^2-36x+7=0

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Solution for 9x^2-36x+7=0 equation:


Simplifying
9x2 + -36x + 7 = 0

Reorder the terms:
7 + -36x + 9x2 = 0

Solving
7 + -36x + 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'.
0.7777777778 + -4x + x2 = 0

Move the constant term to the right:

Add '-0.7777777778' to each side of the equation.
0.7777777778 + -4x + -0.7777777778 + x2 = 0 + -0.7777777778

Reorder the terms:
0.7777777778 + -0.7777777778 + -4x + x2 = 0 + -0.7777777778

Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000
0.0000000000 + -4x + x2 = 0 + -0.7777777778
-4x + x2 = 0 + -0.7777777778

Combine like terms: 0 + -0.7777777778 = -0.7777777778
-4x + x2 = -0.7777777778

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -0.7777777778 + 4

Reorder the terms:
4 + -4x + x2 = -0.7777777778 + 4

Combine like terms: -0.7777777778 + 4 = 3.2222222222
4 + -4x + x2 = 3.2222222222

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3.2222222222

Calculate the square root of the right side: 1.795054936

Break this problem into two subproblems by setting 
(x + -2) equal to 1.795054936 and -1.795054936.

Subproblem 1

x + -2 = 1.795054936 Simplifying x + -2 = 1.795054936 Reorder the terms: -2 + x = 1.795054936 Solving -2 + x = 1.795054936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.795054936 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.795054936 + 2 x = 1.795054936 + 2 Combine like terms: 1.795054936 + 2 = 3.795054936 x = 3.795054936 Simplifying x = 3.795054936

Subproblem 2

x + -2 = -1.795054936 Simplifying x + -2 = -1.795054936 Reorder the terms: -2 + x = -1.795054936 Solving -2 + x = -1.795054936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.795054936 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.795054936 + 2 x = -1.795054936 + 2 Combine like terms: -1.795054936 + 2 = 0.204945064 x = 0.204945064 Simplifying x = 0.204945064

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.795054936, 0.204945064}

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