x^2+.25x=1.25

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Solution for x^2+.25x=1.25 equation: 


Simplifying
x2 + 0.25x = 1.25

Reorder the terms:
0.25x + x2 = 1.25

Solving
0.25x + x2 = 1.25

Solving for variable 'x'.

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

Combine like terms: 1.25 + -1.25 = 0.00
-1.25 + 0.25x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.25x + 1.25 + x2 = 0.00 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.25x + x2 = 0.00 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.25x + x2 = 0.00 + 1.25
0.25x + x2 = 0.00 + 1.25

Combine like terms: 0.00 + 1.25 = 1.25
0.25x + x2 = 1.25

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 = 1.25 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 1.25 + 0.015625

Combine like terms: 1.25 + 0.015625 = 1.265625
0.015625 + 0.25x + x2 = 1.265625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 1.265625

Calculate the square root of the right side: 1.125

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.125 and -1.125.


Subproblem 1
x + 0.125 = 1.125

Simplifying
x + 0.125 = 1.125

Reorder the terms:
0.125 + x = 1.125

Solving
0.125 + x = 1.125

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 = 1.125 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 1.125 + -0.125
x = 1.125 + -0.125

Combine like terms: 1.125 + -0.125 = 1
x = 1

Simplifying
x = 1


Subproblem 2
x + 0.125 = -1.125

Simplifying
x + 0.125 = -1.125

Reorder the terms:
0.125 + x = -1.125

Solving
0.125 + x = -1.125

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 = -1.125 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -1.125 + -0.125
x = -1.125 + -0.125

Combine like terms: -1.125 + -0.125 = -1.25
x = -1.25

Simplifying
x = -1.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, -1.25}

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