8x^2-32x+31=0

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Solution for 8x^2-32x+31=0 equation:


Simplifying
8x2 + -32x + 31 = 0

Reorder the terms:
31 + -32x + 8x2 = 0

Solving
31 + -32x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
3.875 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.875' to each side of the equation.
3.875 + -4x + -3.875 + x2 = 0 + -3.875

Reorder the terms:
3.875 + -3.875 + -4x + x2 = 0 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + -4x + x2 = 0 + -3.875
-4x + x2 = 0 + -3.875

Combine like terms: 0 + -3.875 = -3.875
-4x + x2 = -3.875

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 = -3.875 + 4

Reorder the terms:
4 + -4x + x2 = -3.875 + 4

Combine like terms: -3.875 + 4 = 0.125
4 + -4x + x2 = 0.125

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(x + -2) equal to 0.353553391 and -0.353553391.

Subproblem 1

x + -2 = 0.353553391 Simplifying x + -2 = 0.353553391 Reorder the terms: -2 + x = 0.353553391 Solving -2 + x = 0.353553391 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 = 0.353553391 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.353553391 + 2 x = 0.353553391 + 2 Combine like terms: 0.353553391 + 2 = 2.353553391 x = 2.353553391 Simplifying x = 2.353553391

Subproblem 2

x + -2 = -0.353553391 Simplifying x + -2 = -0.353553391 Reorder the terms: -2 + x = -0.353553391 Solving -2 + x = -0.353553391 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 = -0.353553391 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.353553391 + 2 x = -0.353553391 + 2 Combine like terms: -0.353553391 + 2 = 1.646446609 x = 1.646446609 Simplifying x = 1.646446609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.353553391, 1.646446609}

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