X^2+7X-2.25=0

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Solution for X^2+7X-2.25=0 equation: 


Simplifying
X2 + 7X + -2.25 = 0

Reorder the terms:
-2.25 + 7X + X2 = 0

Solving
-2.25 + 7X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 7X + 2.25 + X2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 7X + X2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 7X + X2 = 0 + 2.25
7X + X2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
7X + X2 = 2.25

The X term is 7X.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7X + 12.25 + X2 = 2.25 + 12.25

Reorder the terms:
12.25 + 7X + X2 = 2.25 + 12.25

Combine like terms: 2.25 + 12.25 = 14.5
12.25 + 7X + X2 = 14.5

Factor a perfect square on the left side:
(X + 3.5)(X + 3.5) = 14.5

Calculate the square root of the right side: 3.807886553

Break this problem into two subproblems by setting 
(X + 3.5) equal to 3.807886553 and -3.807886553.


Subproblem 1
X + 3.5 = 3.807886553

Simplifying
X + 3.5 = 3.807886553

Reorder the terms:
3.5 + X = 3.807886553

Solving
3.5 + X = 3.807886553

Solving for variable 'X'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + X = 3.807886553 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + X = 3.807886553 + -3.5
X = 3.807886553 + -3.5

Combine like terms: 3.807886553 + -3.5 = 0.307886553
X = 0.307886553

Simplifying
X = 0.307886553


Subproblem 2
X + 3.5 = -3.807886553

Simplifying
X + 3.5 = -3.807886553

Reorder the terms:
3.5 + X = -3.807886553

Solving
3.5 + X = -3.807886553

Solving for variable 'X'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + X = -3.807886553 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + X = -3.807886553 + -3.5
X = -3.807886553 + -3.5

Combine like terms: -3.807886553 + -3.5 = -7.307886553
X = -7.307886553

Simplifying
X = -7.307886553


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.307886553, -7.307886553}

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