x(-9.7-x)=23.22

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Solution for x(-9.7-x)=23.22 equation: 


Simplifying
x(-9.7 + -1x) = 23.22
(-9.7 * x + -1x * x) = 23.22
(-9.7x + -1x2) = 23.22

Solving
-9.7x + -1x2 = 23.22

Solving for variable 'x'.

Reorder the terms:
-23.22 + -9.7x + -1x2 = 23.22 + -23.22

Combine like terms: 23.22 + -23.22 = 0.00
-23.22 + -9.7x + -1x2 = 0.00

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

Divide each side by '-1'.
23.22 + 9.7x + x2 = 0.00

Move the constant term to the right:

Add '-23.22' to each side of the equation.
23.22 + 9.7x + -23.22 + x2 = 0.00 + -23.22

Reorder the terms:
23.22 + -23.22 + 9.7x + x2 = 0.00 + -23.22

Combine like terms: 23.22 + -23.22 = 0.00
0.00 + 9.7x + x2 = 0.00 + -23.22
9.7x + x2 = 0.00 + -23.22

Combine like terms: 0.00 + -23.22 = -23.22
9.7x + x2 = -23.22

The x term is 9.7x.  Take half its coefficient (4.85).
Square it (23.5225) and add it to both sides.

Add '23.5225' to each side of the equation.
9.7x + 23.5225 + x2 = -23.22 + 23.5225

Reorder the terms:
23.5225 + 9.7x + x2 = -23.22 + 23.5225

Combine like terms: -23.22 + 23.5225 = 0.3025
23.5225 + 9.7x + x2 = 0.3025

Factor a perfect square on the left side:
(x + 4.85)(x + 4.85) = 0.3025

Calculate the square root of the right side: 0.55

Break this problem into two subproblems by setting 
(x + 4.85) equal to 0.55 and -0.55.


Subproblem 1
x + 4.85 = 0.55

Simplifying
x + 4.85 = 0.55

Reorder the terms:
4.85 + x = 0.55

Solving
4.85 + x = 0.55

Solving for variable 'x'.

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

Add '-4.85' to each side of the equation.
4.85 + -4.85 + x = 0.55 + -4.85

Combine like terms: 4.85 + -4.85 = 0.00
0.00 + x = 0.55 + -4.85
x = 0.55 + -4.85

Combine like terms: 0.55 + -4.85 = -4.3
x = -4.3

Simplifying
x = -4.3


Subproblem 2
x + 4.85 = -0.55

Simplifying
x + 4.85 = -0.55

Reorder the terms:
4.85 + x = -0.55

Solving
4.85 + x = -0.55

Solving for variable 'x'.

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

Add '-4.85' to each side of the equation.
4.85 + -4.85 + x = -0.55 + -4.85

Combine like terms: 4.85 + -4.85 = 0.00
0.00 + x = -0.55 + -4.85
x = -0.55 + -4.85

Combine like terms: -0.55 + -4.85 = -5.4
x = -5.4

Simplifying
x = -5.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.3, -5.4}

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