53.3x^2-75.62x+26.117=0

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Solution for 53.3x^2-75.62x+26.117=0 equation:


Simplifying
53.3x2 + -75.62x + 26.117 = 0

Reorder the terms:
26.117 + -75.62x + 53.3x2 = 0

Solving
26.117 + -75.62x + 53.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '53.3'.
0.49 + -1.418761726x + x2 = 0

Move the constant term to the right:

Add '-0.49' to each side of the equation.
0.49 + -1.418761726x + -0.49 + x2 = 0 + -0.49

Reorder the terms:
0.49 + -0.49 + -1.418761726x + x2 = 0 + -0.49

Combine like terms: 0.49 + -0.49 = 0.00
0.00 + -1.418761726x + x2 = 0 + -0.49
-1.418761726x + x2 = 0 + -0.49

Combine like terms: 0 + -0.49 = -0.49
-1.418761726x + x2 = -0.49

The x term is -1.418761726x.  Take half its coefficient (-0.709380863).
Square it (0.5032212088) and add it to both sides.

Add '0.5032212088' to each side of the equation.
-1.418761726x + 0.5032212088 + x2 = -0.49 + 0.5032212088

Reorder the terms:
0.5032212088 + -1.418761726x + x2 = -0.49 + 0.5032212088

Combine like terms: -0.49 + 0.5032212088 = 0.0132212088
0.5032212088 + -1.418761726x + x2 = 0.0132212088

Factor a perfect square on the left side:
(x + -0.709380863)(x + -0.709380863) = 0.0132212088

Calculate the square root of the right side: 0.114983515

Break this problem into two subproblems by setting 
(x + -0.709380863) equal to 0.114983515 and -0.114983515.

Subproblem 1

x + -0.709380863 = 0.114983515 Simplifying x + -0.709380863 = 0.114983515 Reorder the terms: -0.709380863 + x = 0.114983515 Solving -0.709380863 + x = 0.114983515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.709380863' to each side of the equation. -0.709380863 + 0.709380863 + x = 0.114983515 + 0.709380863 Combine like terms: -0.709380863 + 0.709380863 = 0.000000000 0.000000000 + x = 0.114983515 + 0.709380863 x = 0.114983515 + 0.709380863 Combine like terms: 0.114983515 + 0.709380863 = 0.824364378 x = 0.824364378 Simplifying x = 0.824364378

Subproblem 2

x + -0.709380863 = -0.114983515 Simplifying x + -0.709380863 = -0.114983515 Reorder the terms: -0.709380863 + x = -0.114983515 Solving -0.709380863 + x = -0.114983515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.709380863' to each side of the equation. -0.709380863 + 0.709380863 + x = -0.114983515 + 0.709380863 Combine like terms: -0.709380863 + 0.709380863 = 0.000000000 0.000000000 + x = -0.114983515 + 0.709380863 x = -0.114983515 + 0.709380863 Combine like terms: -0.114983515 + 0.709380863 = 0.594397348 x = 0.594397348 Simplifying x = 0.594397348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.824364378, 0.594397348}

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