x^2-.25x+.0625=2+.0625

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Solution for x^2-.25x+.0625=2+.0625 equation:


Simplifying
x2 + -0.25x + 0.0625 = 2 + 0.0625

Reorder the terms:
0.0625 + -0.25x + x2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + -0.25x + x2 = 2.0625

Solving
0.0625 + -0.25x + x2 = 2.0625

Solving for variable 'x'.

Reorder the terms:
0.0625 + -2.0625 + -0.25x + x2 = 2.0625 + -2.0625

Combine like terms: 0.0625 + -2.0625 = -2
-2 + -0.25x + x2 = 2.0625 + -2.0625

Combine like terms: 2.0625 + -2.0625 = 0.0000
-2 + -0.25x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.25x + 2 + x2 = 0.0000 + 2

Reorder the terms:
-2 + 2 + -0.25x + x2 = 0.0000 + 2

Combine like terms: -2 + 2 = 0
0 + -0.25x + x2 = 0.0000 + 2
-0.25x + x2 = 0.0000 + 2

Combine like terms: 0.0000 + 2 = 2
-0.25x + x2 = 2

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 = 2 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 2 + 0.015625

Combine like terms: 2 + 0.015625 = 2.015625
0.015625 + -0.25x + x2 = 2.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.419727086 and -1.419727086.

Subproblem 1

x + -0.125 = 1.419727086 Simplifying x + -0.125 = 1.419727086 Reorder the terms: -0.125 + x = 1.419727086 Solving -0.125 + x = 1.419727086 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 = 1.419727086 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.419727086 + 0.125 x = 1.419727086 + 0.125 Combine like terms: 1.419727086 + 0.125 = 1.544727086 x = 1.544727086 Simplifying x = 1.544727086

Subproblem 2

x + -0.125 = -1.419727086 Simplifying x + -0.125 = -1.419727086 Reorder the terms: -0.125 + x = -1.419727086 Solving -0.125 + x = -1.419727086 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 = -1.419727086 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.419727086 + 0.125 x = -1.419727086 + 0.125 Combine like terms: -1.419727086 + 0.125 = -1.294727086 x = -1.294727086 Simplifying x = -1.294727086

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.544727086, -1.294727086}

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