-2x(x+2)+4=-6

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Solution for -2x(x+2)+4=-6 equation: 


Simplifying
-2x(x + 2) + 4 = -6

Reorder the terms:
-2x(2 + x) + 4 = -6
(2 * -2x + x * -2x) + 4 = -6
(-4x + -2x2) + 4 = -6

Reorder the terms:
4 + -4x + -2x2 = -6

Solving
4 + -4x + -2x2 = -6

Solving for variable 'x'.

Reorder the terms:
4 + 6 + -4x + -2x2 = -6 + 6

Combine like terms: 4 + 6 = 10
10 + -4x + -2x2 = -6 + 6

Combine like terms: -6 + 6 = 0
10 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -2x + -1x2 = 0

Solving
5 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 2x + x2 = 0

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}
Solution
x = {1.449489743, -3.449489743}

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