1=x^2+16x+61

Solution for 1=x^2+16x+61 equation:

Simplifying
1 = x2 + 16x + 61

Reorder the terms:
1 = 61 + 16x + x2

Solving
1 = 61 + 16x + x2

Solving for variable 'x'.

Combine like terms: 1 + -61 = -60
-60 + -16x + -1x2 = 61 + 16x + x2 + -61 + -16x + -1x2

Reorder the terms:
-60 + -16x + -1x2 = 61 + -61 + 16x + -16x + x2 + -1x2

Combine like terms: 61 + -61 = 0
-60 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2
-60 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-60 + -16x + -1x2 = 0 + x2 + -1x2
-60 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-60 + -16x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(60 + 16x + x2) = 0

Factor a trinomial.
-1((10 + x)(6 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-10, -6}