566(6+x)x+5=

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Solution for 566(6+x)x+5= equation:


Simplifying
566(6 + x) * x + 5 = 0

Reorder the terms for easier multiplication:
566x(6 + x) + 5 = 0
(6 * 566x + x * 566x) + 5 = 0
(3396x + 566x2) + 5 = 0

Reorder the terms:
5 + 3396x + 566x2 = 0

Solving
5 + 3396x + 566x2 = 0

Solving for variable 'x'.

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

Divide each side by '566'.
0.008833922261 + 6x + x2 = 0

Move the constant term to the right:

Add '-0.008833922261' to each side of the equation.
0.008833922261 + 6x + -0.008833922261 + x2 = 0 + -0.008833922261

Reorder the terms:
0.008833922261 + -0.008833922261 + 6x + x2 = 0 + -0.008833922261

Combine like terms: 0.008833922261 + -0.008833922261 = 0.000000000000
0.000000000000 + 6x + x2 = 0 + -0.008833922261
6x + x2 = 0 + -0.008833922261

Combine like terms: 0 + -0.008833922261 = -0.008833922261
6x + x2 = -0.008833922261

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -0.008833922261 + 9

Reorder the terms:
9 + 6x + x2 = -0.008833922261 + 9

Combine like terms: -0.008833922261 + 9 = 8.991166077739
9 + 6x + x2 = 8.991166077739

Factor a perfect square on the left side:
(x + 3)(x + 3) = 8.991166077739

Calculate the square root of the right side: 2.998527318

Break this problem into two subproblems by setting 
(x + 3) equal to 2.998527318 and -2.998527318.


Subproblem 1
x + 3 = 2.998527318

Simplifying
x + 3 = 2.998527318

Reorder the terms:
3 + x = 2.998527318

Solving
3 + x = 2.998527318

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.998527318 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.998527318 + -3
x = 2.998527318 + -3

Combine like terms: 2.998527318 + -3 = -0.001472682
x = -0.001472682

Simplifying
x = -0.001472682


Subproblem 2
x + 3 = -2.998527318

Simplifying
x + 3 = -2.998527318

Reorder the terms:
3 + x = -2.998527318

Solving
3 + x = -2.998527318

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.998527318 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.998527318 + -3
x = -2.998527318 + -3

Combine like terms: -2.998527318 + -3 = -5.998527318
x = -5.998527318

Simplifying
x = -5.998527318


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.001472682, -5.998527318}

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