25x^2+350x+2500=5000

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Solution for 25x^2+350x+2500=5000 equation: 


Simplifying
25x2 + 350x + 2500 = 5000

Reorder the terms:
2500 + 350x + 25x2 = 5000

Solving
2500 + 350x + 25x2 = 5000

Solving for variable 'x'.

Reorder the terms:
2500 + -5000 + 350x + 25x2 = 5000 + -5000

Combine like terms: 2500 + -5000 = -2500
-2500 + 350x + 25x2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-2500 + 350x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-100 + 14x + x2) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(-100 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + 14x + x2 = 0

Solving
-100 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 14x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 14x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 14x + x2 = 0 + 100
14x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
14x + x2 = 100

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 100 + 49

Reorder the terms:
49 + 14x + x2 = 100 + 49

Combine like terms: 100 + 49 = 149
49 + 14x + x2 = 149

Factor a perfect square on the left side:
(x + 7)(x + 7) = 149

Calculate the square root of the right side: 12.206555616

Break this problem into two subproblems by setting 
(x + 7) equal to 12.206555616 and -12.206555616.


Subproblem 1
x + 7 = 12.206555616

Simplifying
x + 7 = 12.206555616

Reorder the terms:
7 + x = 12.206555616

Solving
7 + x = 12.206555616

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 12.206555616 + -7

Combine like terms: 7 + -7 = 0
0 + x = 12.206555616 + -7
x = 12.206555616 + -7

Combine like terms: 12.206555616 + -7 = 5.206555616
x = 5.206555616

Simplifying
x = 5.206555616


Subproblem 2
x + 7 = -12.206555616

Simplifying
x + 7 = -12.206555616

Reorder the terms:
7 + x = -12.206555616

Solving
7 + x = -12.206555616

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -12.206555616 + -7

Combine like terms: 7 + -7 = 0
0 + x = -12.206555616 + -7
x = -12.206555616 + -7

Combine like terms: -12.206555616 + -7 = -19.206555616
x = -19.206555616

Simplifying
x = -19.206555616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.206555616, -19.206555616}
Solution
x = {5.206555616, -19.206555616}

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