(x+2)=7-x(x+1)

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Solution for (x+2)=7-x(x+1) equation: 


Simplifying
(x + 2) = 7 + -1x(x + 1)

Reorder the terms:
(2 + x) = 7 + -1x(x + 1)

Remove parenthesis around (2 + x)
2 + x = 7 + -1x(x + 1)

Reorder the terms:
2 + x = 7 + -1x(1 + x)
2 + x = 7 + (1 * -1x + x * -1x)
2 + x = 7 + (-1x + -1x2)

Solving
2 + x = 7 + -1x + -1x2

Solving for variable 'x'.

Reorder the terms:
2 + -7 + x + x + x2 = 7 + -1x + -1x2 + -7 + x + x2

Combine like terms: 2 + -7 = -5
-5 + x + x + x2 = 7 + -1x + -1x2 + -7 + x + x2

Combine like terms: x + x = 2x
-5 + 2x + x2 = 7 + -1x + -1x2 + -7 + x + x2

Reorder the terms:
-5 + 2x + x2 = 7 + -7 + -1x + x + -1x2 + x2

Combine like terms: 7 + -7 = 0
-5 + 2x + x2 = 0 + -1x + x + -1x2 + x2
-5 + 2x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-5 + 2x + x2 = 0 + -1x2 + x2
-5 + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-5 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 2x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x + x2 = 0 + 5
2x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
2x + x2 = 5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 5 + 1

Reorder the terms:
1 + 2x + x2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2x + x2 = 6

Factor a perfect square on the left side:
(x + 1)(x + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 1) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 1 = 2.449489743

Simplifying
x + 1 = 2.449489743

Reorder the terms:
1 + x = 2.449489743

Solving
1 + x = 2.449489743

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.449489743 + -1
x = 2.449489743 + -1

Combine like terms: 2.449489743 + -1 = 1.449489743
x = 1.449489743

Simplifying
x = 1.449489743


Subproblem 2
x + 1 = -2.449489743

Simplifying
x + 1 = -2.449489743

Reorder the terms:
1 + x = -2.449489743

Solving
1 + x = -2.449489743

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.449489743 + -1
x = -2.449489743 + -1

Combine like terms: -2.449489743 + -1 = -3.449489743
x = -3.449489743

Simplifying
x = -3.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.449489743, -3.449489743}

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