x^2-6.25x-0.625=0

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Solution for x^2-6.25x-0.625=0 equation: 


Simplifying
x2 + -6.25x + -0.625 = 0

Reorder the terms:
-0.625 + -6.25x + x2 = 0

Solving
-0.625 + -6.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -6.25x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -6.25x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -6.25x + x2 = 0 + 0.625
-6.25x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-6.25x + x2 = 0.625

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = 0.625 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = 0.625 + 9.765625

Combine like terms: 0.625 + 9.765625 = 10.390625
9.765625 + -6.25x + x2 = 10.390625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 10.390625

Calculate the square root of the right side: 3.22344924

Break this problem into two subproblems by setting 
(x + -3.125) equal to 3.22344924 and -3.22344924.


Subproblem 1
x + -3.125 = 3.22344924

Simplifying
x + -3.125 = 3.22344924

Reorder the terms:
-3.125 + x = 3.22344924

Solving
-3.125 + x = 3.22344924

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 3.22344924 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 3.22344924 + 3.125
x = 3.22344924 + 3.125

Combine like terms: 3.22344924 + 3.125 = 6.34844924
x = 6.34844924

Simplifying
x = 6.34844924


Subproblem 2
x + -3.125 = -3.22344924

Simplifying
x + -3.125 = -3.22344924

Reorder the terms:
-3.125 + x = -3.22344924

Solving
-3.125 + x = -3.22344924

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -3.22344924 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -3.22344924 + 3.125
x = -3.22344924 + 3.125

Combine like terms: -3.22344924 + 3.125 = -0.09844924
x = -0.09844924

Simplifying
x = -0.09844924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.34844924, -0.09844924}

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