5x(x+9)-2(1-x)=1

Solution for 5x(x+9)-2(1-x)=1 equation:

Simplifying
5x(x + 9) + -2(1 + -1x) = 1

Reorder the terms:
5x(9 + x) + -2(1 + -1x) = 1
(9 * 5x + x * 5x) + -2(1 + -1x) = 1
(45x + 5x2) + -2(1 + -1x) = 1
45x + 5x2 + (1 * -2 + -1x * -2) = 1
45x + 5x2 + (-2 + 2x) = 1

Reorder the terms:
-2 + 45x + 2x + 5x2 = 1

Combine like terms: 45x + 2x = 47x
-2 + 47x + 5x2 = 1

Solving
-2 + 47x + 5x2 = 1

Solving for variable 'x'.

Reorder the terms:
-2 + -1 + 47x + 5x2 = 1 + -1

Combine like terms: -2 + -1 = -3
-3 + 47x + 5x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + 47x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + 9.4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 9.4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 9.4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 9.4x + x2 = 0 + 0.6
9.4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
9.4x + x2 = 0.6

The x term is 9.4x.  Take half its coefficient (4.7).
Square it (22.09) and add it to both sides.

Add '22.09' to each side of the equation.
9.4x + 22.09 + x2 = 0.6 + 22.09

Reorder the terms:
22.09 + 9.4x + x2 = 0.6 + 22.09

Combine like terms: 0.6 + 22.09 = 22.69
22.09 + 9.4x + x2 = 22.69

Factor a perfect square on the left side:
(x + 4.7)(x + 4.7) = 22.69

Calculate the square root of the right side: 4.763402146

Break this problem into two subproblems by setting 
(x + 4.7) equal to 4.763402146 and -4.763402146.

Subproblem 1
x + 4.7 = 4.763402146

Simplifying
x + 4.7 = 4.763402146

Reorder the terms:
4.7 + x = 4.763402146

Solving
4.7 + x = 4.763402146

Solving for variable 'x'.

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

Add '-4.7' to each side of the equation.
4.7 + -4.7 + x = 4.763402146 + -4.7

Combine like terms: 4.7 + -4.7 = 0.0
0.0 + x = 4.763402146 + -4.7
x = 4.763402146 + -4.7

Combine like terms: 4.763402146 + -4.7 = 0.063402146
x = 0.063402146

Simplifying
x = 0.063402146

Subproblem 2
x + 4.7 = -4.763402146

Simplifying
x + 4.7 = -4.763402146

Reorder the terms:
4.7 + x = -4.763402146

Solving
4.7 + x = -4.763402146

Solving for variable 'x'.

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

Add '-4.7' to each side of the equation.
4.7 + -4.7 + x = -4.763402146 + -4.7

Combine like terms: 4.7 + -4.7 = 0.0
0.0 + x = -4.763402146 + -4.7
x = -4.763402146 + -4.7

Combine like terms: -4.763402146 + -4.7 = -9.463402146
x = -9.463402146

Simplifying
x = -9.463402146

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.063402146, -9.463402146}