(2x-9)(2x-9)-1=0

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Solution for (2x-9)(2x-9)-1=0 equation: 


Simplifying
(2x + -9)(2x + -9) + -1 = 0

Reorder the terms:
(-9 + 2x)(2x + -9) + -1 = 0

Reorder the terms:
(-9 + 2x)(-9 + 2x) + -1 = 0

Multiply (-9 + 2x) * (-9 + 2x)
(-9(-9 + 2x) + 2x * (-9 + 2x)) + -1 = 0
((-9 * -9 + 2x * -9) + 2x * (-9 + 2x)) + -1 = 0
((81 + -18x) + 2x * (-9 + 2x)) + -1 = 0
(81 + -18x + (-9 * 2x + 2x * 2x)) + -1 = 0
(81 + -18x + (-18x + 4x2)) + -1 = 0

Combine like terms: -18x + -18x = -36x
(81 + -36x + 4x2) + -1 = 0

Reorder the terms:
81 + -1 + -36x + 4x2 = 0

Combine like terms: 81 + -1 = 80
80 + -36x + 4x2 = 0

Solving
80 + -36x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -9x + x2) = 0

Factor a trinomial.
4((4 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {4, 5}

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