0.25x^2-0.46x-3.1=0

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Solution for 0.25x^2-0.46x-3.1=0 equation: 


Simplifying
0.25x2 + -0.46x + -3.1 = 0

Reorder the terms:
-3.1 + -0.46x + 0.25x2 = 0

Solving
-3.1 + -0.46x + 0.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.25 the coefficient of the squared term: 

Divide each side by '0.25'.
-12.4 + -1.84x + x2 = 0

Move the constant term to the right:

Add '12.4' to each side of the equation.
-12.4 + -1.84x + 12.4 + x2 = 0 + 12.4

Reorder the terms:
-12.4 + 12.4 + -1.84x + x2 = 0 + 12.4

Combine like terms: -12.4 + 12.4 = 0.0
0.0 + -1.84x + x2 = 0 + 12.4
-1.84x + x2 = 0 + 12.4

Combine like terms: 0 + 12.4 = 12.4
-1.84x + x2 = 12.4

The x term is -1.84x.  Take half its coefficient (-0.92).
Square it (0.8464) and add it to both sides.

Add '0.8464' to each side of the equation.
-1.84x + 0.8464 + x2 = 12.4 + 0.8464

Reorder the terms:
0.8464 + -1.84x + x2 = 12.4 + 0.8464

Combine like terms: 12.4 + 0.8464 = 13.2464
0.8464 + -1.84x + x2 = 13.2464

Factor a perfect square on the left side:
(x + -0.92)(x + -0.92) = 13.2464

Calculate the square root of the right side: 3.639560413

Break this problem into two subproblems by setting 
(x + -0.92) equal to 3.639560413 and -3.639560413.


Subproblem 1
x + -0.92 = 3.639560413

Simplifying
x + -0.92 = 3.639560413

Reorder the terms:
-0.92 + x = 3.639560413

Solving
-0.92 + x = 3.639560413

Solving for variable 'x'.

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

Add '0.92' to each side of the equation.
-0.92 + 0.92 + x = 3.639560413 + 0.92

Combine like terms: -0.92 + 0.92 = 0.00
0.00 + x = 3.639560413 + 0.92
x = 3.639560413 + 0.92

Combine like terms: 3.639560413 + 0.92 = 4.559560413
x = 4.559560413

Simplifying
x = 4.559560413


Subproblem 2
x + -0.92 = -3.639560413

Simplifying
x + -0.92 = -3.639560413

Reorder the terms:
-0.92 + x = -3.639560413

Solving
-0.92 + x = -3.639560413

Solving for variable 'x'.

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

Add '0.92' to each side of the equation.
-0.92 + 0.92 + x = -3.639560413 + 0.92

Combine like terms: -0.92 + 0.92 = 0.00
0.00 + x = -3.639560413 + 0.92
x = -3.639560413 + 0.92

Combine like terms: -3.639560413 + 0.92 = -2.719560413
x = -2.719560413

Simplifying
x = -2.719560413


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.559560413, -2.719560413}

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