0=x^2+16x+71

Solution for 0=x^2+16x+71 equation:

Simplifying
0 = x2 + 16x + 71

Reorder the terms:
0 = 71 + 16x + x2

Solving
0 = 71 + 16x + x2

Solving for variable 'x'.

Combine like terms: 0 + -71 = -71
-71 + -16x + -1x2 = 71 + 16x + x2 + -71 + -16x + -1x2

Reorder the terms:
-71 + -16x + -1x2 = 71 + -71 + 16x + -16x + x2 + -1x2

Combine like terms: 71 + -71 = 0
-71 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2
-71 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-71 + -16x + -1x2 = 0 + x2 + -1x2
-71 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-71 + -16x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(71 + 16x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(71 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
71 + 16x + x2 = 0

Solving
71 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-71' to each side of the equation.
71 + 16x + -71 + x2 = 0 + -71

Reorder the terms:
71 + -71 + 16x + x2 = 0 + -71

Combine like terms: 71 + -71 = 0
0 + 16x + x2 = 0 + -71
16x + x2 = 0 + -71

Combine like terms: 0 + -71 = -71
16x + x2 = -71

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -71 + 64

Reorder the terms:
64 + 16x + x2 = -71 + 64

Combine like terms: -71 + 64 = -7
64 + 16x + x2 = -7

Factor a perfect square on the left side:
(x + 8)(x + 8) = -7

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.