(5x-1)(5x-1)=36

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Solution for (5x-1)(5x-1)=36 equation:


Simplifying
(5x + -1)(5x + -1) = 36

Reorder the terms:
(-1 + 5x)(5x + -1) = 36

Reorder the terms:
(-1 + 5x)(-1 + 5x) = 36

Multiply (-1 + 5x) * (-1 + 5x)
(-1(-1 + 5x) + 5x * (-1 + 5x)) = 36
((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 36
((1 + -5x) + 5x * (-1 + 5x)) = 36
(1 + -5x + (-1 * 5x + 5x * 5x)) = 36
(1 + -5x + (-5x + 25x2)) = 36

Combine like terms: -5x + -5x = -10x
(1 + -10x + 25x2) = 36

Solving
1 + -10x + 25x2 = 36

Solving for variable 'x'.

Reorder the terms:
1 + -36 + -10x + 25x2 = 36 + -36

Combine like terms: 1 + -36 = -35
-35 + -10x + 25x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-35 + -10x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -2x + 5x2) = 0

Factor a trinomial.
5((-1 + -1x)(7 + -5x)) = 0

Ignore the factor 5.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {-1, 1.4}

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