9x+9x*x=2

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Solution for 9x+9x*x=2 equation:


Simplifying
9x + 9x * x = 2

Multiply x * x
9x + 9x2 = 2

Solving
9x + 9x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 9x + 9x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 9x + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.2222222222
x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
x + x2 = 0.2222222222

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.2222222222 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.2222222222 + 0.25

Combine like terms: 0.2222222222 + 0.25 = 0.4722222222
1.25 + x2 = 0.4722222222

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.4722222222

Calculate the square root of the right side: 0.687184271

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.687184271 and -0.687184271.

Subproblem 1

x + 0.5 = 0.687184271 Simplifying x + 0.5 = 0.687184271 Reorder the terms: 0.5 + x = 0.687184271 Solving 0.5 + x = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.687184271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.687184271 + -0.5 x = 0.687184271 + -0.5 Combine like terms: 0.687184271 + -0.5 = 0.187184271 x = 0.187184271 Simplifying x = 0.187184271

Subproblem 2

x + 0.5 = -0.687184271 Simplifying x + 0.5 = -0.687184271 Reorder the terms: 0.5 + x = -0.687184271 Solving 0.5 + x = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.687184271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.687184271 + -0.5 x = -0.687184271 + -0.5 Combine like terms: -0.687184271 + -0.5 = -1.187184271 x = -1.187184271 Simplifying x = -1.187184271

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.187184271, -1.187184271}

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