4x^2-2x+1=9

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Solution for 4x^2-2x+1=9 equation: 


Simplifying
4x2 + -2x + 1 = 9

Reorder the terms:
1 + -2x + 4x2 = 9

Solving
1 + -2x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
1 + -9 + -2x + 4x2 = 9 + -9

Combine like terms: 1 + -9 = -8
-8 + -2x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-8 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -1x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x + 2x2 = 0

Solving
-4 + -1x + 2x2 = 0

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

Divide each side by '2'.
-2 + -0.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.5x + x2 = 0 + 2
-0.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.5x + x2 = 2

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 2 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + -0.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.436140662 and -1.436140662.


Subproblem 1
x + -0.25 = 1.436140662

Simplifying
x + -0.25 = 1.436140662

Reorder the terms:
-0.25 + x = 1.436140662

Solving
-0.25 + x = 1.436140662

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 1.436140662 + 0.25
x = 1.436140662 + 0.25

Combine like terms: 1.436140662 + 0.25 = 1.686140662
x = 1.686140662

Simplifying
x = 1.686140662


Subproblem 2
x + -0.25 = -1.436140662

Simplifying
x + -0.25 = -1.436140662

Reorder the terms:
-0.25 + x = -1.436140662

Solving
-0.25 + x = -1.436140662

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -1.436140662 + 0.25
x = -1.436140662 + 0.25

Combine like terms: -1.436140662 + 0.25 = -1.186140662
x = -1.186140662

Simplifying
x = -1.186140662


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.686140662, -1.186140662}
Solution
x = {1.686140662, -1.186140662}

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