X^2+3X-2=7

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Solution for X^2+3X-2=7 equation: 


Simplifying
X2 + 3X + -2 = 7

Reorder the terms:
-2 + 3X + X2 = 7

Solving
-2 + 3X + X2 = 7

Solving for variable 'X'.

Reorder the terms:
-2 + -7 + 3X + X2 = 7 + -7

Combine like terms: -2 + -7 = -9
-9 + 3X + X2 = 7 + -7

Combine like terms: 7 + -7 = 0
-9 + 3X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 3X + 9 + X2 = 0 + 9

Reorder the terms:
-9 + 9 + 3X + X2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 3X + X2 = 0 + 9
3X + X2 = 0 + 9

Combine like terms: 0 + 9 = 9
3X + X2 = 9

The X term is 3X.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3X + 2.25 + X2 = 9 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + 3X + X2 = 11.25

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(X + 1.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
X + 1.5 = 3.354101966

Simplifying
X + 1.5 = 3.354101966

Reorder the terms:
1.5 + X = 3.354101966

Solving
1.5 + X = 3.354101966

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = 3.354101966 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = 3.354101966 + -1.5
X = 3.354101966 + -1.5

Combine like terms: 3.354101966 + -1.5 = 1.854101966
X = 1.854101966

Simplifying
X = 1.854101966


Subproblem 2
X + 1.5 = -3.354101966

Simplifying
X + 1.5 = -3.354101966

Reorder the terms:
1.5 + X = -3.354101966

Solving
1.5 + X = -3.354101966

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = -3.354101966 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = -3.354101966 + -1.5
X = -3.354101966 + -1.5

Combine like terms: -3.354101966 + -1.5 = -4.854101966
X = -4.854101966

Simplifying
X = -4.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.854101966, -4.854101966}

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