s^2+2s+5=53

Solution for s^2+2s+5=53 equation:

Simplifying
s2 + 2s + 5 = 53

Reorder the terms:
5 + 2s + s2 = 53

Solving
5 + 2s + s2 = 53

Solving for variable 's'.

Reorder the terms:
5 + -53 + 2s + s2 = 53 + -53

Combine like terms: 5 + -53 = -48
-48 + 2s + s2 = 53 + -53

Combine like terms: 53 + -53 = 0
-48 + 2s + s2 = 0

Factor a trinomial.
(-8 + -1s)(6 + -1s) = 0

Subproblem 1
Set the factor '(-8 + -1s)' equal to zero and attempt to solve:

Simplifying
-8 + -1s = 0

Solving
-8 + -1s = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1s = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1s = 0 + 8
-1s = 0 + 8

Combine like terms: 0 + 8 = 8
-1s = 8

Divide each side by '-1'.
s = -8

Simplifying
s = -8
Subproblem 2
Set the factor '(6 + -1s)' equal to zero and attempt to solve:

Simplifying
6 + -1s = 0

Solving
6 + -1s = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1s = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1s = 0 + -6
-1s = 0 + -6

Combine like terms: 0 + -6 = -6
-1s = -6

Divide each side by '-1'.
s = 6

Simplifying
s = 6
Solution
s = {-8, 6}