x^2-.25x+.015=0

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Solution for x^2-.25x+.015=0 equation:


Simplifying
x2 + -0.25x + 0.015 = 0

Reorder the terms:
0.015 + -0.25x + x2 = 0

Solving
0.015 + -0.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.015' to each side of the equation.
0.015 + -0.25x + -0.015 + x2 = 0 + -0.015

Reorder the terms:
0.015 + -0.015 + -0.25x + x2 = 0 + -0.015

Combine like terms: 0.015 + -0.015 = 0.000
0.000 + -0.25x + x2 = 0 + -0.015
-0.25x + x2 = 0 + -0.015

Combine like terms: 0 + -0.015 = -0.015
-0.25x + x2 = -0.015

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = -0.015 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = -0.015 + 0.015625

Combine like terms: -0.015 + 0.015625 = 0.000625
0.015625 + -0.25x + x2 = 0.000625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.000625

Calculate the square root of the right side: 0.025

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.025 and -0.025.

Subproblem 1

x + -0.125 = 0.025 Simplifying x + -0.125 = 0.025 Reorder the terms: -0.125 + x = 0.025 Solving -0.125 + x = 0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.025 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.025 + 0.125 x = 0.025 + 0.125 Combine like terms: 0.025 + 0.125 = 0.15 x = 0.15 Simplifying x = 0.15

Subproblem 2

x + -0.125 = -0.025 Simplifying x + -0.125 = -0.025 Reorder the terms: -0.125 + x = -0.025 Solving -0.125 + x = -0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.025 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.025 + 0.125 x = -0.025 + 0.125 Combine like terms: -0.025 + 0.125 = 0.1 x = 0.1 Simplifying x = 0.1

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.15, 0.1}

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