2x(x+4)=-3.5

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Solution for 2x(x+4)=-3.5 equation: 


Simplifying
2x(x + 4) = -3.5

Reorder the terms:
2x(4 + x) = -3.5
(4 * 2x + x * 2x) = -3.5
(8x + 2x2) = -3.5

Solving
8x + 2x2 = -3.5

Solving for variable 'x'.

Reorder the terms:
3.5 + 8x + 2x2 = -3.5 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
3.5 + 8x + 2x2 = 0.0

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

Divide each side by '2'.
1.75 + 4x + x2 = 0.0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 4x + -1.75 + x2 = 0.0 + -1.75

Reorder the terms:
1.75 + -1.75 + 4x + x2 = 0.0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 4x + x2 = 0.0 + -1.75
4x + x2 = 0.0 + -1.75

Combine like terms: 0.0 + -1.75 = -1.75
4x + x2 = -1.75

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1.75 + 4

Reorder the terms:
4 + 4x + x2 = -1.75 + 4

Combine like terms: -1.75 + 4 = 2.25
4 + 4x + x2 = 2.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + 2) equal to 1.5 and -1.5.


Subproblem 1
x + 2 = 1.5

Simplifying
x + 2 = 1.5

Reorder the terms:
2 + x = 1.5

Solving
2 + x = 1.5

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.5 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.5 + -2
x = 1.5 + -2

Combine like terms: 1.5 + -2 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 2 = -1.5

Simplifying
x + 2 = -1.5

Reorder the terms:
2 + x = -1.5

Solving
2 + x = -1.5

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.5 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.5 + -2
x = -1.5 + -2

Combine like terms: -1.5 + -2 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -3.5}

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