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

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


Simplifying
0 = (5x + -1)(5x + -1)

Reorder the terms:
0 = (-1 + 5x)(5x + -1)

Reorder the terms:
0 = (-1 + 5x)(-1 + 5x)

Multiply (-1 + 5x) * (-1 + 5x)
0 = (-1(-1 + 5x) + 5x * (-1 + 5x))
0 = ((-1 * -1 + 5x * -1) + 5x * (-1 + 5x))
0 = ((1 + -5x) + 5x * (-1 + 5x))
0 = (1 + -5x + (-1 * 5x + 5x * 5x))
0 = (1 + -5x + (-5x + 25x2))

Combine like terms: -5x + -5x = -10x
0 = (1 + -10x + 25x2)

Solving
0 = 1 + -10x + 25x2

Solving for variable 'x'.

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

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

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

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

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

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

Subproblem 1

Set the factor '(-1 + 5x)' equal to zero and attempt to solve: Simplifying -1 + 5x = 0 Solving -1 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5x = 0 + 1 5x = 0 + 1 Combine like terms: 0 + 1 = 1 5x = 1 Divide each side by '5'. x = 0.2 Simplifying x = 0.2

Subproblem 2

Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2

Solution

x = {0.2, 0.2}

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