X^2+7X+12=4X+14

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Solution for X^2+7X+12=4X+14 equation: 


Simplifying
X2 + 7X + 12 = 4X + 14

Reorder the terms:
12 + 7X + X2 = 4X + 14

Reorder the terms:
12 + 7X + X2 = 14 + 4X

Solving
12 + 7X + X2 = 14 + 4X

Solving for variable 'X'.

Reorder the terms:
12 + -14 + 7X + -4X + X2 = 14 + 4X + -14 + -4X

Combine like terms: 12 + -14 = -2
-2 + 7X + -4X + X2 = 14 + 4X + -14 + -4X

Combine like terms: 7X + -4X = 3X
-2 + 3X + X2 = 14 + 4X + -14 + -4X

Reorder the terms:
-2 + 3X + X2 = 14 + -14 + 4X + -4X

Combine like terms: 14 + -14 = 0
-2 + 3X + X2 = 0 + 4X + -4X
-2 + 3X + X2 = 4X + -4X

Combine like terms: 4X + -4X = 0
-2 + 3X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3X + 2 + X2 = 0 + 2

Reorder the terms:
-2 + 2 + 3X + X2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3X + X2 = 0 + 2
3X + X2 = 0 + 2

Combine like terms: 0 + 2 = 2
3X + X2 = 2

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 = 2 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3X + X2 = 4.25

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(X + 1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
X + 1.5 = 2.061552813

Simplifying
X + 1.5 = 2.061552813

Reorder the terms:
1.5 + X = 2.061552813

Solving
1.5 + X = 2.061552813

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 = 2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = 2.061552813 + -1.5
X = 2.061552813 + -1.5

Combine like terms: 2.061552813 + -1.5 = 0.561552813
X = 0.561552813

Simplifying
X = 0.561552813


Subproblem 2
X + 1.5 = -2.061552813

Simplifying
X + 1.5 = -2.061552813

Reorder the terms:
1.5 + X = -2.061552813

Solving
1.5 + X = -2.061552813

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 = -2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = -2.061552813 + -1.5
X = -2.061552813 + -1.5

Combine like terms: -2.061552813 + -1.5 = -3.561552813
X = -3.561552813

Simplifying
X = -3.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.561552813, -3.561552813}

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