x^2+7x-21=0

Solution for x^2+7x-21=0 equation:

Simplifying
x2 + 7x + -21 = 0

Reorder the terms:
-21 + 7x + x2 = 0

Solving
-21 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 7x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 7x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 7x + x2 = 0 + 21
7x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
7x + x2 = 21

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 = 21 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 21 + 12.25

Combine like terms: 21 + 12.25 = 33.25
12.25 + 7x + x2 = 33.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
x + 3.5 = 5.766281297

Simplifying
x + 3.5 = 5.766281297

Reorder the terms:
3.5 + x = 5.766281297

Solving
3.5 + x = 5.766281297

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.766281297 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.766281297 + -3.5
x = 5.766281297 + -3.5

Combine like terms: 5.766281297 + -3.5 = 2.266281297
x = 2.266281297

Simplifying
x = 2.266281297

Subproblem 2
x + 3.5 = -5.766281297

Simplifying
x + 3.5 = -5.766281297

Reorder the terms:
3.5 + x = -5.766281297

Solving
3.5 + x = -5.766281297

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.766281297 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.766281297 + -3.5
x = -5.766281297 + -3.5

Combine like terms: -5.766281297 + -3.5 = -9.266281297
x = -9.266281297

Simplifying
x = -9.266281297

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.266281297, -9.266281297}