36x^2-99x+1=0

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Solution for 36x^2-99x+1=0 equation:


Simplifying
36x2 + -99x + 1 = 0

Reorder the terms:
1 + -99x + 36x2 = 0

Solving
1 + -99x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
0.02777777778 + -2.75x + x2 = 0

Move the constant term to the right:

Add '-0.02777777778' to each side of the equation.
0.02777777778 + -2.75x + -0.02777777778 + x2 = 0 + -0.02777777778

Reorder the terms:
0.02777777778 + -0.02777777778 + -2.75x + x2 = 0 + -0.02777777778

Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000
0.00000000000 + -2.75x + x2 = 0 + -0.02777777778
-2.75x + x2 = 0 + -0.02777777778

Combine like terms: 0 + -0.02777777778 = -0.02777777778
-2.75x + x2 = -0.02777777778

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = -0.02777777778 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = -0.02777777778 + 1.890625

Combine like terms: -0.02777777778 + 1.890625 = 1.86284722222
1.890625 + -2.75x + x2 = 1.86284722222

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = 1.86284722222

Calculate the square root of the right side: 1.364861613

Break this problem into two subproblems by setting 
(x + -1.375) equal to 1.364861613 and -1.364861613.

Subproblem 1

x + -1.375 = 1.364861613 Simplifying x + -1.375 = 1.364861613 Reorder the terms: -1.375 + x = 1.364861613 Solving -1.375 + x = 1.364861613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.364861613 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.364861613 + 1.375 x = 1.364861613 + 1.375 Combine like terms: 1.364861613 + 1.375 = 2.739861613 x = 2.739861613 Simplifying x = 2.739861613

Subproblem 2

x + -1.375 = -1.364861613 Simplifying x + -1.375 = -1.364861613 Reorder the terms: -1.375 + x = -1.364861613 Solving -1.375 + x = -1.364861613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.364861613 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.364861613 + 1.375 x = -1.364861613 + 1.375 Combine like terms: -1.364861613 + 1.375 = 0.010138387 x = 0.010138387 Simplifying x = 0.010138387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.739861613, 0.010138387}

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