9x^2+3x-2=1

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Solution for 9x^2+3x-2=1 equation: 


Simplifying
9x2 + 3x + -2 = 1

Reorder the terms:
-2 + 3x + 9x2 = 1

Solving
-2 + 3x + 9x2 = 1

Solving for variable 'x'.

Reorder the terms:
-2 + -1 + 3x + 9x2 = 1 + -1

Combine like terms: -2 + -1 = -3
-3 + 3x + 9x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + 3x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + x + 3x2 = 0

Solving
-1 + x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.3333333333x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.3333333333x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + 0.3333333333
0.3333333333x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.3333333333x + x2 = 0.3333333333

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.
0.3333333333x + 0.25 + x2 = 0.3333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 0.3333333333 + 0.25

Combine like terms: 0.3333333333 + 0.25 = 0.5833333333
0.25 + 0.3333333333x + x2 = 0.5833333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.5833333333

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.763762616 and -0.763762616.


Subproblem 1
x + 0.5 = 0.763762616

Simplifying
x + 0.5 = 0.763762616

Reorder the terms:
0.5 + x = 0.763762616

Solving
0.5 + x = 0.763762616

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 = 0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.763762616 + -0.5
x = 0.763762616 + -0.5

Combine like terms: 0.763762616 + -0.5 = 0.263762616
x = 0.263762616

Simplifying
x = 0.263762616


Subproblem 2
x + 0.5 = -0.763762616

Simplifying
x + 0.5 = -0.763762616

Reorder the terms:
0.5 + x = -0.763762616

Solving
0.5 + x = -0.763762616

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 = -0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.763762616 + -0.5
x = -0.763762616 + -0.5

Combine like terms: -0.763762616 + -0.5 = -1.263762616
x = -1.263762616

Simplifying
x = -1.263762616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.263762616, -1.263762616}
Solution
x = {0.263762616, -1.263762616}

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