X^2+5X+6.25=8.5

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Solution for X^2+5X+6.25=8.5 equation: 


Simplifying
X2 + 5X + 6.25 = 8.5

Reorder the terms:
6.25 + 5X + X2 = 8.5

Solving
6.25 + 5X + X2 = 8.5

Solving for variable 'X'.

Reorder the terms:
6.25 + -8.5 + 5X + X2 = 8.5 + -8.5

Combine like terms: 6.25 + -8.5 = -2.25
-2.25 + 5X + X2 = 8.5 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
-2.25 + 5X + X2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 5X + 2.25 + X2 = 0.0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 5X + X2 = 0.0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 5X + X2 = 0.0 + 2.25
5X + X2 = 0.0 + 2.25

Combine like terms: 0.0 + 2.25 = 2.25
5X + X2 = 2.25

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 = 2.25 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 2.25 + 6.25

Combine like terms: 2.25 + 6.25 = 8.5
6.25 + 5X + X2 = 8.5

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(X + 2.5) equal to 2.915475947 and -2.915475947.


Subproblem 1
X + 2.5 = 2.915475947

Simplifying
X + 2.5 = 2.915475947

Reorder the terms:
2.5 + X = 2.915475947

Solving
2.5 + X = 2.915475947

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 = 2.915475947 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 2.915475947 + -2.5
X = 2.915475947 + -2.5

Combine like terms: 2.915475947 + -2.5 = 0.415475947
X = 0.415475947

Simplifying
X = 0.415475947


Subproblem 2
X + 2.5 = -2.915475947

Simplifying
X + 2.5 = -2.915475947

Reorder the terms:
2.5 + X = -2.915475947

Solving
2.5 + X = -2.915475947

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 = -2.915475947 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -2.915475947 + -2.5
X = -2.915475947 + -2.5

Combine like terms: -2.915475947 + -2.5 = -5.415475947
X = -5.415475947

Simplifying
X = -5.415475947


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.415475947, -5.415475947}

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