2x^2-30x+9=81

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Solution for 2x^2-30x+9=81 equation: 


Simplifying
2x2 + -30x + 9 = 81

Reorder the terms:
9 + -30x + 2x2 = 81

Solving
9 + -30x + 2x2 = 81

Solving for variable 'x'.

Reorder the terms:
9 + -81 + -30x + 2x2 = 81 + -81

Combine like terms: 9 + -81 = -72
-72 + -30x + 2x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-72 + -30x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -15x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + -15x + x2 = 0

Solving
-36 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -15x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -15x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -15x + x2 = 0 + 36
-15x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-15x + x2 = 36

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 36 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 36 + 56.25

Combine like terms: 36 + 56.25 = 92.25
56.25 + -15x + x2 = 92.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + -7.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
x + -7.5 = 9.604686356

Simplifying
x + -7.5 = 9.604686356

Reorder the terms:
-7.5 + x = 9.604686356

Solving
-7.5 + x = 9.604686356

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 9.604686356 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 9.604686356 + 7.5
x = 9.604686356 + 7.5

Combine like terms: 9.604686356 + 7.5 = 17.104686356
x = 17.104686356

Simplifying
x = 17.104686356


Subproblem 2
x + -7.5 = -9.604686356

Simplifying
x + -7.5 = -9.604686356

Reorder the terms:
-7.5 + x = -9.604686356

Solving
-7.5 + x = -9.604686356

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -9.604686356 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -9.604686356 + 7.5
x = -9.604686356 + 7.5

Combine like terms: -9.604686356 + 7.5 = -2.104686356
x = -2.104686356

Simplifying
x = -2.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.104686356, -2.104686356}
Solution
x = {17.104686356, -2.104686356}

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