x(x+8.9)=-18.7

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Solution for x(x+8.9)=-18.7 equation: 


Simplifying
x(x + 8.9) = -18.7

Reorder the terms:
x(8.9 + x) = -18.7
(8.9 * x + x * x) = -18.7
(8.9x + x2) = -18.7

Solving
8.9x + x2 = -18.7

Solving for variable 'x'.

Reorder the terms:
18.7 + 8.9x + x2 = -18.7 + 18.7

Combine like terms: -18.7 + 18.7 = 0.0
18.7 + 8.9x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-18.7' to each side of the equation.
18.7 + 8.9x + -18.7 + x2 = 0.0 + -18.7

Reorder the terms:
18.7 + -18.7 + 8.9x + x2 = 0.0 + -18.7

Combine like terms: 18.7 + -18.7 = 0.0
0.0 + 8.9x + x2 = 0.0 + -18.7
8.9x + x2 = 0.0 + -18.7

Combine like terms: 0.0 + -18.7 = -18.7
8.9x + x2 = -18.7

The x term is 8.9x.  Take half its coefficient (4.45).
Square it (19.8025) and add it to both sides.

Add '19.8025' to each side of the equation.
8.9x + 19.8025 + x2 = -18.7 + 19.8025

Reorder the terms:
19.8025 + 8.9x + x2 = -18.7 + 19.8025

Combine like terms: -18.7 + 19.8025 = 1.1025
19.8025 + 8.9x + x2 = 1.1025

Factor a perfect square on the left side:
(x + 4.45)(x + 4.45) = 1.1025

Calculate the square root of the right side: 1.05

Break this problem into two subproblems by setting 
(x + 4.45) equal to 1.05 and -1.05.


Subproblem 1
x + 4.45 = 1.05

Simplifying
x + 4.45 = 1.05

Reorder the terms:
4.45 + x = 1.05

Solving
4.45 + x = 1.05

Solving for variable 'x'.

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

Add '-4.45' to each side of the equation.
4.45 + -4.45 + x = 1.05 + -4.45

Combine like terms: 4.45 + -4.45 = 0.00
0.00 + x = 1.05 + -4.45
x = 1.05 + -4.45

Combine like terms: 1.05 + -4.45 = -3.4
x = -3.4

Simplifying
x = -3.4


Subproblem 2
x + 4.45 = -1.05

Simplifying
x + 4.45 = -1.05

Reorder the terms:
4.45 + x = -1.05

Solving
4.45 + x = -1.05

Solving for variable 'x'.

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

Add '-4.45' to each side of the equation.
4.45 + -4.45 + x = -1.05 + -4.45

Combine like terms: 4.45 + -4.45 = 0.00
0.00 + x = -1.05 + -4.45
x = -1.05 + -4.45

Combine like terms: -1.05 + -4.45 = -5.5
x = -5.5

Simplifying
x = -5.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.4, -5.5}

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