(7x-5)(7x-5)=25

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Solution for (7x-5)(7x-5)=25 equation: 


Simplifying
(7x + -5)(7x + -5) = 25

Reorder the terms:
(-5 + 7x)(7x + -5) = 25

Reorder the terms:
(-5 + 7x)(-5 + 7x) = 25

Multiply (-5 + 7x) * (-5 + 7x)
(-5(-5 + 7x) + 7x * (-5 + 7x)) = 25
((-5 * -5 + 7x * -5) + 7x * (-5 + 7x)) = 25
((25 + -35x) + 7x * (-5 + 7x)) = 25
(25 + -35x + (-5 * 7x + 7x * 7x)) = 25
(25 + -35x + (-35x + 49x2)) = 25

Combine like terms: -35x + -35x = -70x
(25 + -70x + 49x2) = 25

Add '-25' to each side of the equation.
25 + -70x + -25 + 49x2 = 25 + -25

Reorder the terms:
25 + -25 + -70x + 49x2 = 25 + -25

Combine like terms: 25 + -25 = 0
0 + -70x + 49x2 = 25 + -25
-70x + 49x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-70x + 49x2 = 0

Solving
-70x + 49x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x'.
7x(-10 + 7x) = 0

Ignore the factor 7.

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 '(-10 + 7x)' equal to zero and attempt to solve:

Simplifying
-10 + 7x = 0

Solving
-10 + 7x = 0

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

Add '10' to each side of the equation.
-10 + 10 + 7x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 7x = 0 + 10
7x = 0 + 10

Combine like terms: 0 + 10 = 10
7x = 10

Divide each side by '7'.
x = 1.428571429

Simplifying
x = 1.428571429
Solution
x = {0, 1.428571429}

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