0=x^2+7x+42

Solution for 0=x^2+7x+42 equation:

Simplifying
0 = x2 + 7x + 42

Reorder the terms:
0 = 42 + 7x + x2

Solving
0 = 42 + 7x + x2

Solving for variable 'x'.

Combine like terms: 0 + -42 = -42
-42 + -7x + -1x2 = 42 + 7x + x2 + -42 + -7x + -1x2

Reorder the terms:
-42 + -7x + -1x2 = 42 + -42 + 7x + -7x + x2 + -1x2

Combine like terms: 42 + -42 = 0
-42 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
-42 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-42 + -7x + -1x2 = 0 + x2 + -1x2
-42 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(42 + 7x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(42 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
42 + 7x + x2 = 0

Solving
42 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + 7x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + 7x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 7x + x2 = 0 + -42
7x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
7x + x2 = -42

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -42 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -42 + 12.25

Combine like terms: -42 + 12.25 = -29.75
12.25 + 7x + x2 = -29.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = -29.75

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.