X(X-2)+3=5-7X

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Solution for X(X-2)+3=5-7X equation: 


Simplifying
X(X + -2) + 3 = 5 + -7X

Reorder the terms:
X(-2 + X) + 3 = 5 + -7X
(-2 * X + X * X) + 3 = 5 + -7X
(-2X + X2) + 3 = 5 + -7X

Reorder the terms:
3 + -2X + X2 = 5 + -7X

Solving
3 + -2X + X2 = 5 + -7X

Solving for variable 'X'.

Reorder the terms:
3 + -5 + -2X + 7X + X2 = 5 + -7X + -5 + 7X

Combine like terms: 3 + -5 = -2
-2 + -2X + 7X + X2 = 5 + -7X + -5 + 7X

Combine like terms: -2X + 7X = 5X
-2 + 5X + X2 = 5 + -7X + -5 + 7X

Reorder the terms:
-2 + 5X + X2 = 5 + -5 + -7X + 7X

Combine like terms: 5 + -5 = 0
-2 + 5X + X2 = 0 + -7X + 7X
-2 + 5X + X2 = -7X + 7X

Combine like terms: -7X + 7X = 0
-2 + 5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 5X + 2 + X2 = 0 + 2

Reorder the terms:
-2 + 2 + 5X + X2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5X + X2 = 0 + 2
5X + X2 = 0 + 2

Combine like terms: 0 + 2 = 2
5X + X2 = 2

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 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + 5X + X2 = 8.25

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(X + 2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
X + 2.5 = 2.872281323

Simplifying
X + 2.5 = 2.872281323

Reorder the terms:
2.5 + X = 2.872281323

Solving
2.5 + X = 2.872281323

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 = 2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 2.872281323 + -2.5
X = 2.872281323 + -2.5

Combine like terms: 2.872281323 + -2.5 = 0.372281323
X = 0.372281323

Simplifying
X = 0.372281323


Subproblem 2
X + 2.5 = -2.872281323

Simplifying
X + 2.5 = -2.872281323

Reorder the terms:
2.5 + X = -2.872281323

Solving
2.5 + X = -2.872281323

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 = -2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -2.872281323 + -2.5
X = -2.872281323 + -2.5

Combine like terms: -2.872281323 + -2.5 = -5.372281323
X = -5.372281323

Simplifying
X = -5.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.372281323, -5.372281323}

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