(5x-1)(5x-1)=1

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Solution for (5x-1)(5x-1)=1 equation: 


Simplifying
(5x + -1)(5x + -1) = 1

Reorder the terms:
(-1 + 5x)(5x + -1) = 1

Reorder the terms:
(-1 + 5x)(-1 + 5x) = 1

Multiply (-1 + 5x) * (-1 + 5x)
(-1(-1 + 5x) + 5x * (-1 + 5x)) = 1
((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 1
((1 + -5x) + 5x * (-1 + 5x)) = 1
(1 + -5x + (-1 * 5x + 5x * 5x)) = 1
(1 + -5x + (-5x + 25x2)) = 1

Combine like terms: -5x + -5x = -10x
(1 + -10x + 25x2) = 1

Add '-1' to each side of the equation.
1 + -10x + -1 + 25x2 = 1 + -1

Reorder the terms:
1 + -1 + -10x + 25x2 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + -10x + 25x2 = 1 + -1
-10x + 25x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-10x + 25x2 = 0

Solving
-10x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-2 + 5x) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-2 + 5x = 0

Solving
-2 + 5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x = 0 + 2
5x = 0 + 2

Combine like terms: 0 + 2 = 2
5x = 2

Divide each side by '5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {0, 0.4}

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