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

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 = 0
(-81 + 0 + 4x2) + -1 = 0
(-81 + 4x2) + -1 = 0

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

Combine like terms: -81 + -1 = -82
-82 + 4x2 = 0

Solving
-82 + 4x2 = 0

Solving for variable 'x'.

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

Add '82' to each side of the equation.
-82 + 82 + 4x2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + 4x2 = 0 + 82
4x2 = 0 + 82

Combine like terms: 0 + 82 = 82
4x2 = 82

Divide each side by '4'.
x2 = 20.5

Simplifying
x2 = 20.5

Take the square root of each side:
x = {-4.527692569, 4.527692569}