x^2-1.265x-(0.0625)=0

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Solution for x^2-1.265x-(0.0625)=0 equation:


Simplifying
x2 + -1.265x + -1(0.0625) = 0

Multiply -1 * 0.0625
x2 + -1.265x + -0.0625 = 0

Reorder the terms:
-0.0625 + -1.265x + x2 = 0

Solving
-0.0625 + -1.265x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -1.265x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -1.265x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -1.265x + x2 = 0 + 0.0625
-1.265x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-1.265x + x2 = 0.0625

The x term is -1.265x.  Take half its coefficient (-0.6325).
Square it (0.40005625) and add it to both sides.

Add '0.40005625' to each side of the equation.
-1.265x + 0.40005625 + x2 = 0.0625 + 0.40005625

Reorder the terms:
0.40005625 + -1.265x + x2 = 0.0625 + 0.40005625

Combine like terms: 0.0625 + 0.40005625 = 0.46255625
0.40005625 + -1.265x + x2 = 0.46255625

Factor a perfect square on the left side:
(x + -0.6325)(x + -0.6325) = 0.46255625

Calculate the square root of the right side: 0.68011488

Break this problem into two subproblems by setting 
(x + -0.6325) equal to 0.68011488 and -0.68011488.


Subproblem 1
x + -0.6325 = 0.68011488

Simplifying
x + -0.6325 = 0.68011488

Reorder the terms:
-0.6325 + x = 0.68011488

Solving
-0.6325 + x = 0.68011488

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.6325' to each side of the equation.
-0.6325 + 0.6325 + x = 0.68011488 + 0.6325

Combine like terms: -0.6325 + 0.6325 = 0.0000
0.0000 + x = 0.68011488 + 0.6325
x = 0.68011488 + 0.6325

Combine like terms: 0.68011488 + 0.6325 = 1.31261488
x = 1.31261488

Simplifying
x = 1.31261488


Subproblem 2
x + -0.6325 = -0.68011488

Simplifying
x + -0.6325 = -0.68011488

Reorder the terms:
-0.6325 + x = -0.68011488

Solving
-0.6325 + x = -0.68011488

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.6325' to each side of the equation.
-0.6325 + 0.6325 + x = -0.68011488 + 0.6325

Combine like terms: -0.6325 + 0.6325 = 0.0000
0.0000 + x = -0.68011488 + 0.6325
x = -0.68011488 + 0.6325

Combine like terms: -0.68011488 + 0.6325 = -0.04761488
x = -0.04761488

Simplifying
x = -0.04761488


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.31261488, -0.04761488}

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