=x^2+100x+2500

Solution for =x^2+100x+2500 equation:

Simplifying
0 = x2 + 100x + 2500

Reorder the terms:
0 = 2500 + 100x + x2

Solving
0 = 2500 + 100x + x2

Solving for variable 'x'.

Combine like terms: 0 + -2500 = -2500
-2500 + -100x + -1x2 = 2500 + 100x + x2 + -2500 + -100x + -1x2

Reorder the terms:
-2500 + -100x + -1x2 = 2500 + -2500 + 100x + -100x + x2 + -1x2

Combine like terms: 2500 + -2500 = 0
-2500 + -100x + -1x2 = 0 + 100x + -100x + x2 + -1x2
-2500 + -100x + -1x2 = 100x + -100x + x2 + -1x2

Combine like terms: 100x + -100x = 0
-2500 + -100x + -1x2 = 0 + x2 + -1x2
-2500 + -100x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2500 + -100x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2500 + 100x + x2) = 0

Factor a trinomial.
-1((50 + x)(50 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(50 + x)' equal to zero and attempt to solve:

Simplifying
50 + x = 0

Solving
50 + x = 0

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

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

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

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

Simplifying
x = -50
Subproblem 2
Set the factor '(50 + x)' equal to zero and attempt to solve:

Simplifying
50 + x = 0

Solving
50 + x = 0

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

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

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

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

Simplifying
x = -50
Solution
x = {-50, -50}