x^2-0.0474x+0.000276=0

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Solution for x^2-0.0474x+0.000276=0 equation:


Simplifying
x2 + -0.0474x + 0.000276 = 0

Reorder the terms:
0.000276 + -0.0474x + x2 = 0

Solving
0.000276 + -0.0474x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.000276' to each side of the equation.
0.000276 + -0.0474x + -0.000276 + x2 = 0 + -0.000276

Reorder the terms:
0.000276 + -0.000276 + -0.0474x + x2 = 0 + -0.000276

Combine like terms: 0.000276 + -0.000276 = 0.000000
0.000000 + -0.0474x + x2 = 0 + -0.000276
-0.0474x + x2 = 0 + -0.000276

Combine like terms: 0 + -0.000276 = -0.000276
-0.0474x + x2 = -0.000276

The x term is -0.0474x.  Take half its coefficient (-0.0237).
Square it (0.00056169) and add it to both sides.

Add '0.00056169' to each side of the equation.
-0.0474x + 0.00056169 + x2 = -0.000276 + 0.00056169

Reorder the terms:
0.00056169 + -0.0474x + x2 = -0.000276 + 0.00056169

Combine like terms: -0.000276 + 0.00056169 = 0.00028569
0.00056169 + -0.0474x + x2 = 0.00028569

Factor a perfect square on the left side:
(x + -0.0237)(x + -0.0237) = 0.00028569

Calculate the square root of the right side: 0.016902367

Break this problem into two subproblems by setting 
(x + -0.0237) equal to 0.016902367 and -0.016902367.

Subproblem 1

x + -0.0237 = 0.016902367 Simplifying x + -0.0237 = 0.016902367 Reorder the terms: -0.0237 + x = 0.016902367 Solving -0.0237 + x = 0.016902367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0237' to each side of the equation. -0.0237 + 0.0237 + x = 0.016902367 + 0.0237 Combine like terms: -0.0237 + 0.0237 = 0.0000 0.0000 + x = 0.016902367 + 0.0237 x = 0.016902367 + 0.0237 Combine like terms: 0.016902367 + 0.0237 = 0.040602367 x = 0.040602367 Simplifying x = 0.040602367

Subproblem 2

x + -0.0237 = -0.016902367 Simplifying x + -0.0237 = -0.016902367 Reorder the terms: -0.0237 + x = -0.016902367 Solving -0.0237 + x = -0.016902367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0237' to each side of the equation. -0.0237 + 0.0237 + x = -0.016902367 + 0.0237 Combine like terms: -0.0237 + 0.0237 = 0.0000 0.0000 + x = -0.016902367 + 0.0237 x = -0.016902367 + 0.0237 Combine like terms: -0.016902367 + 0.0237 = 0.006797633 x = 0.006797633 Simplifying x = 0.006797633

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.040602367, 0.006797633}

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