(2x-1)*(2x-1)=625

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Solution for (2x-1)*(2x-1)=625 equation:


Simplifying
(2x + -1)(2x + -1) = 625

Reorder the terms:
(-1 + 2x)(2x + -1) = 625

Reorder the terms:
(-1 + 2x)(-1 + 2x) = 625

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) = 625
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 625
((1 + -2x) + 2x * (-1 + 2x)) = 625
(1 + -2x + (-1 * 2x + 2x * 2x)) = 625
(1 + -2x + (-2x + 4x2)) = 625

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) = 625

Solving
1 + -4x + 4x2 = 625

Solving for variable 'x'.

Reorder the terms:
1 + -625 + -4x + 4x2 = 625 + -625

Combine like terms: 1 + -625 = -624
-624 + -4x + 4x2 = 625 + -625

Combine like terms: 625 + -625 = 0
-624 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-156 + -1x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(13 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-12, 13}

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