x^2+9.2x=-10.5

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Solution for x^2+9.2x=-10.5 equation: 


Simplifying
x2 + 9.2x = -10.5

Reorder the terms:
9.2x + x2 = -10.5

Solving
9.2x + x2 = -10.5

Solving for variable 'x'.

Reorder the terms:
10.5 + 9.2x + x2 = -10.5 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
10.5 + 9.2x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + 9.2x + -10.5 + x2 = 0.0 + -10.5

Reorder the terms:
10.5 + -10.5 + 9.2x + x2 = 0.0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + 9.2x + x2 = 0.0 + -10.5
9.2x + x2 = 0.0 + -10.5

Combine like terms: 0.0 + -10.5 = -10.5
9.2x + x2 = -10.5

The x term is 9.2x.  Take half its coefficient (4.6).
Square it (21.16) and add it to both sides.

Add '21.16' to each side of the equation.
9.2x + 21.16 + x2 = -10.5 + 21.16

Reorder the terms:
21.16 + 9.2x + x2 = -10.5 + 21.16

Combine like terms: -10.5 + 21.16 = 10.66
21.16 + 9.2x + x2 = 10.66

Factor a perfect square on the left side:
(x + 4.6)(x + 4.6) = 10.66

Calculate the square root of the right side: 3.264965543

Break this problem into two subproblems by setting 
(x + 4.6) equal to 3.264965543 and -3.264965543.


Subproblem 1
x + 4.6 = 3.264965543

Simplifying
x + 4.6 = 3.264965543

Reorder the terms:
4.6 + x = 3.264965543

Solving
4.6 + x = 3.264965543

Solving for variable 'x'.

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

Add '-4.6' to each side of the equation.
4.6 + -4.6 + x = 3.264965543 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
0.0 + x = 3.264965543 + -4.6
x = 3.264965543 + -4.6

Combine like terms: 3.264965543 + -4.6 = -1.335034457
x = -1.335034457

Simplifying
x = -1.335034457


Subproblem 2
x + 4.6 = -3.264965543

Simplifying
x + 4.6 = -3.264965543

Reorder the terms:
4.6 + x = -3.264965543

Solving
4.6 + x = -3.264965543

Solving for variable 'x'.

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

Add '-4.6' to each side of the equation.
4.6 + -4.6 + x = -3.264965543 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
0.0 + x = -3.264965543 + -4.6
x = -3.264965543 + -4.6

Combine like terms: -3.264965543 + -4.6 = -7.864965543
x = -7.864965543

Simplifying
x = -7.864965543


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.335034457, -7.864965543}

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