X^2+3.25X-19.25=0

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Solution for X^2+3.25X-19.25=0 equation: 


Simplifying
X2 + 3.25X + -19.25 = 0

Reorder the terms:
-19.25 + 3.25X + X2 = 0

Solving
-19.25 + 3.25X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '19.25' to each side of the equation.
-19.25 + 3.25X + 19.25 + X2 = 0 + 19.25

Reorder the terms:
-19.25 + 19.25 + 3.25X + X2 = 0 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + 3.25X + X2 = 0 + 19.25
3.25X + X2 = 0 + 19.25

Combine like terms: 0 + 19.25 = 19.25
3.25X + X2 = 19.25

The X term is 3.25X.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25X + 2.640625 + X2 = 19.25 + 2.640625

Reorder the terms:
2.640625 + 3.25X + X2 = 19.25 + 2.640625

Combine like terms: 19.25 + 2.640625 = 21.890625
2.640625 + 3.25X + X2 = 21.890625

Factor a perfect square on the left side:
(X + 1.625)(X + 1.625) = 21.890625

Calculate the square root of the right side: 4.678741818

Break this problem into two subproblems by setting 
(X + 1.625) equal to 4.678741818 and -4.678741818.


Subproblem 1
X + 1.625 = 4.678741818

Simplifying
X + 1.625 = 4.678741818

Reorder the terms:
1.625 + X = 4.678741818

Solving
1.625 + X = 4.678741818

Solving for variable 'X'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + X = 4.678741818 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + X = 4.678741818 + -1.625
X = 4.678741818 + -1.625

Combine like terms: 4.678741818 + -1.625 = 3.053741818
X = 3.053741818

Simplifying
X = 3.053741818


Subproblem 2
X + 1.625 = -4.678741818

Simplifying
X + 1.625 = -4.678741818

Reorder the terms:
1.625 + X = -4.678741818

Solving
1.625 + X = -4.678741818

Solving for variable 'X'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + X = -4.678741818 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + X = -4.678741818 + -1.625
X = -4.678741818 + -1.625

Combine like terms: -4.678741818 + -1.625 = -6.303741818
X = -6.303741818

Simplifying
X = -6.303741818


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.053741818, -6.303741818}

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