25(x^2+50x+41)=0

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Solution for 25(x^2+50x+41)=0 equation: 


Simplifying
25(x2 + 50x + 41) = 0

Reorder the terms:
25(41 + 50x + x2) = 0
(41 * 25 + 50x * 25 + x2 * 25) = 0
(1025 + 1250x + 25x2) = 0

Solving
1025 + 1250x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(41 + 50x + x2) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(41 + 50x + x2)' equal to zero and attempt to solve:

Simplifying
41 + 50x + x2 = 0

Solving
41 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + 50x + -41 + x2 = 0 + -41

Reorder the terms:
41 + -41 + 50x + x2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 50x + x2 = 0 + -41
50x + x2 = 0 + -41

Combine like terms: 0 + -41 = -41
50x + x2 = -41

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = -41 + 625

Reorder the terms:
625 + 50x + x2 = -41 + 625

Combine like terms: -41 + 625 = 584
625 + 50x + x2 = 584

Factor a perfect square on the left side:
(x + 25)(x + 25) = 584

Calculate the square root of the right side: 24.166091947

Break this problem into two subproblems by setting 
(x + 25) equal to 24.166091947 and -24.166091947.


Subproblem 1
x + 25 = 24.166091947

Simplifying
x + 25 = 24.166091947

Reorder the terms:
25 + x = 24.166091947

Solving
25 + x = 24.166091947

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 24.166091947 + -25

Combine like terms: 25 + -25 = 0
0 + x = 24.166091947 + -25
x = 24.166091947 + -25

Combine like terms: 24.166091947 + -25 = -0.833908053
x = -0.833908053

Simplifying
x = -0.833908053


Subproblem 2
x + 25 = -24.166091947

Simplifying
x + 25 = -24.166091947

Reorder the terms:
25 + x = -24.166091947

Solving
25 + x = -24.166091947

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -24.166091947 + -25

Combine like terms: 25 + -25 = 0
0 + x = -24.166091947 + -25
x = -24.166091947 + -25

Combine like terms: -24.166091947 + -25 = -49.166091947
x = -49.166091947

Simplifying
x = -49.166091947


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.833908053, -49.166091947}
Solution
x = {-0.833908053, -49.166091947}

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