-0.25*x^2+1.25*x+1=0

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Solution for -0.25*x^2+1.25*x+1=0 equation: 


Simplifying
-0.25x2 + 1.25x + 1 = 0

Reorder the terms:
1 + 1.25x + -0.25x2 = 0

Solving
1 + 1.25x + -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'.
-4 + -5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x + x2 = 0 + 4
-5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-5x + x2 = 4

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 4 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + -5x + x2 = 10.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + -2.5 = 3.201562119

Simplifying
x + -2.5 = 3.201562119

Reorder the terms:
-2.5 + x = 3.201562119

Solving
-2.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.201562119 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.201562119 + 2.5
x = 3.201562119 + 2.5

Combine like terms: 3.201562119 + 2.5 = 5.701562119
x = 5.701562119

Simplifying
x = 5.701562119


Subproblem 2
x + -2.5 = -3.201562119

Simplifying
x + -2.5 = -3.201562119

Reorder the terms:
-2.5 + x = -3.201562119

Solving
-2.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.201562119 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.201562119 + 2.5
x = -3.201562119 + 2.5

Combine like terms: -3.201562119 + 2.5 = -0.701562119
x = -0.701562119

Simplifying
x = -0.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.701562119, -0.701562119}

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