9x^2-2x-52=0

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Solution for 9x^2-2x-52=0 equation: 


Simplifying
9x2 + -2x + -52 = 0

Reorder the terms:
-52 + -2x + 9x2 = 0

Solving
-52 + -2x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-5.777777778 + -0.2222222222x + x2 = 0

Move the constant term to the right:

Add '5.777777778' to each side of the equation.
-5.777777778 + -0.2222222222x + 5.777777778 + x2 = 0 + 5.777777778

Reorder the terms:
-5.777777778 + 5.777777778 + -0.2222222222x + x2 = 0 + 5.777777778

Combine like terms: -5.777777778 + 5.777777778 = 0.000000000
0.000000000 + -0.2222222222x + x2 = 0 + 5.777777778
-0.2222222222x + x2 = 0 + 5.777777778

Combine like terms: 0 + 5.777777778 = 5.777777778
-0.2222222222x + x2 = 5.777777778

The x term is -0.2222222222x.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222x + 0.01234567901 + x2 = 5.777777778 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222x + x2 = 5.777777778 + 0.01234567901

Combine like terms: 5.777777778 + 0.01234567901 = 5.79012345701
0.01234567901 + -0.2222222222x + x2 = 5.79012345701

Factor a perfect square on the left side:
(x + -0.1111111111)(x + -0.1111111111) = 5.79012345701

Calculate the square root of the right side: 2.406267536

Break this problem into two subproblems by setting 
(x + -0.1111111111) equal to 2.406267536 and -2.406267536.


Subproblem 1
x + -0.1111111111 = 2.406267536

Simplifying
x + -0.1111111111 = 2.406267536

Reorder the terms:
-0.1111111111 + x = 2.406267536

Solving
-0.1111111111 + x = 2.406267536

Solving for variable 'x'.

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

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.1111111111 + x = 2.406267536 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + x = 2.406267536 + 0.1111111111
x = 2.406267536 + 0.1111111111

Combine like terms: 2.406267536 + 0.1111111111 = 2.5173786471
x = 2.5173786471

Simplifying
x = 2.5173786471


Subproblem 2
x + -0.1111111111 = -2.406267536

Simplifying
x + -0.1111111111 = -2.406267536

Reorder the terms:
-0.1111111111 + x = -2.406267536

Solving
-0.1111111111 + x = -2.406267536

Solving for variable 'x'.

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

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.1111111111 + x = -2.406267536 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + x = -2.406267536 + 0.1111111111
x = -2.406267536 + 0.1111111111

Combine like terms: -2.406267536 + 0.1111111111 = -2.2951564249
x = -2.2951564249

Simplifying
x = -2.2951564249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5173786471, -2.2951564249}

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