66x^2-55x+7=0

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Solution for 66x^2-55x+7=0 equation:


Simplifying
66x2 + -55x + 7 = 0

Reorder the terms:
7 + -55x + 66x2 = 0

Solving
7 + -55x + 66x2 = 0

Solving for variable 'x'.

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

Divide each side by '66'.
0.1060606061 + -0.8333333333x + x2 = 0

Move the constant term to the right:

Add '-0.1060606061' to each side of the equation.
0.1060606061 + -0.8333333333x + -0.1060606061 + x2 = 0 + -0.1060606061

Reorder the terms:
0.1060606061 + -0.1060606061 + -0.8333333333x + x2 = 0 + -0.1060606061

Combine like terms: 0.1060606061 + -0.1060606061 = 0.0000000000
0.0000000000 + -0.8333333333x + x2 = 0 + -0.1060606061
-0.8333333333x + x2 = 0 + -0.1060606061

Combine like terms: 0 + -0.1060606061 = -0.1060606061
-0.8333333333x + x2 = -0.1060606061

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = -0.1060606061 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = -0.1060606061 + 0.1736111111

Combine like terms: -0.1060606061 + 0.1736111111 = 0.067550505
0.1736111111 + -0.8333333333x + x2 = 0.067550505

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 0.067550505

Calculate the square root of the right side: 0.2599048

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 0.2599048 and -0.2599048.

Subproblem 1

x + -0.4166666667 = 0.2599048 Simplifying x + -0.4166666667 = 0.2599048 Reorder the terms: -0.4166666667 + x = 0.2599048 Solving -0.4166666667 + x = 0.2599048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 0.2599048 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 0.2599048 + 0.4166666667 x = 0.2599048 + 0.4166666667 Combine like terms: 0.2599048 + 0.4166666667 = 0.6765714667 x = 0.6765714667 Simplifying x = 0.6765714667

Subproblem 2

x + -0.4166666667 = -0.2599048 Simplifying x + -0.4166666667 = -0.2599048 Reorder the terms: -0.4166666667 + x = -0.2599048 Solving -0.4166666667 + x = -0.2599048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -0.2599048 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -0.2599048 + 0.4166666667 x = -0.2599048 + 0.4166666667 Combine like terms: -0.2599048 + 0.4166666667 = 0.1567618667 x = 0.1567618667 Simplifying x = 0.1567618667

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6765714667, 0.1567618667}

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