0.5*x^2-0.5*x+18=25

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Solution for 0.5*x^2-0.5*x+18=25 equation: 


Simplifying
0.5x2 + -0.5x + 18 = 25

Reorder the terms:
18 + -0.5x + 0.5x2 = 25

Solving
18 + -0.5x + 0.5x2 = 25

Solving for variable 'x'.

Reorder the terms:
18 + -25 + -0.5x + 0.5x2 = 25 + -25

Combine like terms: 18 + -25 = -7
-7 + -0.5x + 0.5x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-7 + -0.5x + 0.5x2 = 0

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

Divide each side by '0.5'.
-14 + -1x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -1x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -1x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x + x2 = 0 + 14
-1x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-1x + x2 = 14

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 14 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 14 + 0.25

Combine like terms: 14 + 0.25 = 14.25
0.25 + -1x + x2 = 14.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + -0.5 = 3.774917218

Simplifying
x + -0.5 = 3.774917218

Reorder the terms:
-0.5 + x = 3.774917218

Solving
-0.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 3.774917218 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 3.774917218 + 0.5
x = 3.774917218 + 0.5

Combine like terms: 3.774917218 + 0.5 = 4.274917218
x = 4.274917218

Simplifying
x = 4.274917218


Subproblem 2
x + -0.5 = -3.774917218

Simplifying
x + -0.5 = -3.774917218

Reorder the terms:
-0.5 + x = -3.774917218

Solving
-0.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -3.774917218 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -3.774917218 + 0.5
x = -3.774917218 + 0.5

Combine like terms: -3.774917218 + 0.5 = -3.274917218
x = -3.274917218

Simplifying
x = -3.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.274917218, -3.274917218}

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