x^2-.82x+.046=0

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Solution for x^2-.82x+.046=0 equation:


Simplifying
x2 + -0.82x + 0.046 = 0

Reorder the terms:
0.046 + -0.82x + x2 = 0

Solving
0.046 + -0.82x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.046' to each side of the equation.
0.046 + -0.82x + -0.046 + x2 = 0 + -0.046

Reorder the terms:
0.046 + -0.046 + -0.82x + x2 = 0 + -0.046

Combine like terms: 0.046 + -0.046 = 0.000
0.000 + -0.82x + x2 = 0 + -0.046
-0.82x + x2 = 0 + -0.046

Combine like terms: 0 + -0.046 = -0.046
-0.82x + x2 = -0.046

The x term is -0.82x.  Take half its coefficient (-0.41).
Square it (0.1681) and add it to both sides.

Add '0.1681' to each side of the equation.
-0.82x + 0.1681 + x2 = -0.046 + 0.1681

Reorder the terms:
0.1681 + -0.82x + x2 = -0.046 + 0.1681

Combine like terms: -0.046 + 0.1681 = 0.1221
0.1681 + -0.82x + x2 = 0.1221

Factor a perfect square on the left side:
(x + -0.41)(x + -0.41) = 0.1221

Calculate the square root of the right side: 0.349428104

Break this problem into two subproblems by setting 
(x + -0.41) equal to 0.349428104 and -0.349428104.

Subproblem 1

x + -0.41 = 0.349428104 Simplifying x + -0.41 = 0.349428104 Reorder the terms: -0.41 + x = 0.349428104 Solving -0.41 + x = 0.349428104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.41' to each side of the equation. -0.41 + 0.41 + x = 0.349428104 + 0.41 Combine like terms: -0.41 + 0.41 = 0.00 0.00 + x = 0.349428104 + 0.41 x = 0.349428104 + 0.41 Combine like terms: 0.349428104 + 0.41 = 0.759428104 x = 0.759428104 Simplifying x = 0.759428104

Subproblem 2

x + -0.41 = -0.349428104 Simplifying x + -0.41 = -0.349428104 Reorder the terms: -0.41 + x = -0.349428104 Solving -0.41 + x = -0.349428104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.41' to each side of the equation. -0.41 + 0.41 + x = -0.349428104 + 0.41 Combine like terms: -0.41 + 0.41 = 0.00 0.00 + x = -0.349428104 + 0.41 x = -0.349428104 + 0.41 Combine like terms: -0.349428104 + 0.41 = 0.060571896 x = 0.060571896 Simplifying x = 0.060571896

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.759428104, 0.060571896}

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