.25x(x+5)+.10=6.50

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Solution for .25x(x+5)+.10=6.50 equation:


Simplifying
0.25x(x + 5) + 0.10 = 6.50

Reorder the terms:
0.25x(5 + x) + 0.10 = 6.50
(5 * 0.25x + x * 0.25x) + 0.10 = 6.50
(1.25x + 0.25x2) + 0.10 = 6.50

Reorder the terms:
0.10 + 1.25x + 0.25x2 = 6.50

Solving
0.10 + 1.25x + 0.25x2 = 6.50

Solving for variable 'x'.

Reorder the terms:
0.10 + -6.50 + 1.25x + 0.25x2 = 6.50 + -6.50

Combine like terms: 0.10 + -6.50 = -6.4
-6.4 + 1.25x + 0.25x2 = 6.50 + -6.50

Combine like terms: 6.50 + -6.50 = 0.00
-6.4 + 1.25x + 0.25x2 = 0.00

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

Divide each side by '0.25'.
-25.6 + 5x + x2 = 0

Move the constant term to the right:

Add '25.6' to each side of the equation.
-25.6 + 5x + 25.6 + x2 = 0 + 25.6

Reorder the terms:
-25.6 + 25.6 + 5x + x2 = 0 + 25.6

Combine like terms: -25.6 + 25.6 = 0.0
0.0 + 5x + x2 = 0 + 25.6
5x + x2 = 0 + 25.6

Combine like terms: 0 + 25.6 = 25.6
5x + x2 = 25.6

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 = 25.6 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 25.6 + 6.25

Combine like terms: 25.6 + 6.25 = 31.85
6.25 + 5x + x2 = 31.85

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 31.85

Calculate the square root of the right side: 5.643580424

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.643580424 and -5.643580424.


Subproblem 1
x + 2.5 = 5.643580424

Simplifying
x + 2.5 = 5.643580424

Reorder the terms:
2.5 + x = 5.643580424

Solving
2.5 + x = 5.643580424

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 = 5.643580424 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.643580424 + -2.5
x = 5.643580424 + -2.5

Combine like terms: 5.643580424 + -2.5 = 3.143580424
x = 3.143580424

Simplifying
x = 3.143580424


Subproblem 2
x + 2.5 = -5.643580424

Simplifying
x + 2.5 = -5.643580424

Reorder the terms:
2.5 + x = -5.643580424

Solving
2.5 + x = -5.643580424

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 = -5.643580424 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.643580424 + -2.5
x = -5.643580424 + -2.5

Combine like terms: -5.643580424 + -2.5 = -8.143580424
x = -8.143580424

Simplifying
x = -8.143580424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.143580424, -8.143580424}

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