4-x(x+1)=39

Solution for 4-x(x+1)=39 equation:

Simplifying
4 + -1x(x + 1) = 39

Reorder the terms:
4 + -1x(1 + x) = 39
4 + (1 * -1x + x * -1x) = 39
4 + (-1x + -1x2) = 39

Solving
4 + -1x + -1x2 = 39

Solving for variable 'x'.

Reorder the terms:
4 + -39 + -1x + -1x2 = 39 + -39

Combine like terms: 4 + -39 = -35
-35 + -1x + -1x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-35 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(35 + x + x2)' equal to zero and attempt to solve:

Simplifying
35 + x + x2 = 0

Solving
35 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + x + x2 = 0 + -35
x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
x + x2 = -35

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -35 + 0.25

Reorder the terms:
0.25 + x + x2 = -35 + 0.25

Combine like terms: -35 + 0.25 = -34.75
0.25 + x + x2 = -34.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -34.75

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.