2x^2+102x+2601=5625

Solution for 2x^2+102x+2601=5625 equation:

Simplifying
2x2 + 102x + 2601 = 5625

Reorder the terms:
2601 + 102x + 2x2 = 5625

Solving
2601 + 102x + 2x2 = 5625

Solving for variable 'x'.

Reorder the terms:
2601 + -5625 + 102x + 2x2 = 5625 + -5625

Combine like terms: 2601 + -5625 = -3024
-3024 + 102x + 2x2 = 5625 + -5625

Combine like terms: 5625 + -5625 = 0
-3024 + 102x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1512 + 51x + x2) = 0

Factor a trinomial.
2((-72 + -1x)(21 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-72 + -1x)' equal to zero and attempt to solve:

Simplifying
-72 + -1x = 0

Solving
-72 + -1x = 0

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

Add '72' to each side of the equation.
-72 + 72 + -1x = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -1x = 0 + 72
-1x = 0 + 72

Combine like terms: 0 + 72 = 72
-1x = 72

Divide each side by '-1'.
x = -72

Simplifying
x = -72
Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {-72, 21}