4x(x+5)=-14

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Solution for 4x(x+5)=-14 equation: 


Simplifying
4x(x + 5) = -14

Reorder the terms:
4x(5 + x) = -14
(5 * 4x + x * 4x) = -14
(20x + 4x2) = -14

Solving
20x + 4x2 = -14

Solving for variable 'x'.

Reorder the terms:
14 + 20x + 4x2 = -14 + 14

Combine like terms: -14 + 14 = 0
14 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + 10x + 2x2 = 0

Solving
7 + 10x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 5x + x2 = 0 + -3.5
5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
5x + x2 = -3.5

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 = -3.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -3.5 + 6.25

Combine like terms: -3.5 + 6.25 = 2.75
6.25 + 5x + x2 = 2.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
x + 2.5 = 1.658312395

Simplifying
x + 2.5 = 1.658312395

Reorder the terms:
2.5 + x = 1.658312395

Solving
2.5 + x = 1.658312395

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 = 1.658312395 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.658312395 + -2.5
x = 1.658312395 + -2.5

Combine like terms: 1.658312395 + -2.5 = -0.841687605
x = -0.841687605

Simplifying
x = -0.841687605


Subproblem 2
x + 2.5 = -1.658312395

Simplifying
x + 2.5 = -1.658312395

Reorder the terms:
2.5 + x = -1.658312395

Solving
2.5 + x = -1.658312395

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 = -1.658312395 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.658312395 + -2.5
x = -1.658312395 + -2.5

Combine like terms: -1.658312395 + -2.5 = -4.158312395
x = -4.158312395

Simplifying
x = -4.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.841687605, -4.158312395}
Solution
x = {-0.841687605, -4.158312395}

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