(5x+1)(5x+1)=9

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Solution for (5x+1)(5x+1)=9 equation: 


Simplifying
(5x + 1)(5x + 1) = 9

Reorder the terms:
(1 + 5x)(5x + 1) = 9

Reorder the terms:
(1 + 5x)(1 + 5x) = 9

Multiply (1 + 5x) * (1 + 5x)
(1(1 + 5x) + 5x * (1 + 5x)) = 9
((1 * 1 + 5x * 1) + 5x * (1 + 5x)) = 9
((1 + 5x) + 5x * (1 + 5x)) = 9
(1 + 5x + (1 * 5x + 5x * 5x)) = 9
(1 + 5x + (5x + 25x2)) = 9

Combine like terms: 5x + 5x = 10x
(1 + 10x + 25x2) = 9

Solving
1 + 10x + 25x2 = 9

Solving for variable 'x'.

Reorder the terms:
1 + -9 + 10x + 25x2 = 9 + -9

Combine like terms: 1 + -9 = -8
-8 + 10x + 25x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-8 + 10x + 25x2 = 0

Factor a trinomial.
(-4 + -5x)(2 + -5x) = 0


Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

Solving
-4 + -5x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4

Combine like terms: 0 + 4 = 4
-5x = 4

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

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 = {-0.8, 0.4}

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