x^2+8x-21=0

Solution for x^2+8x-21=0 equation:

Simplifying
x2 + 8x + -21 = 0

Reorder the terms:
-21 + 8x + x2 = 0

Solving
-21 + 8x + 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 + 8x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 8x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 8x + x2 = 0 + 21
8x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
8x + x2 = 21

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 21 + 16

Reorder the terms:
16 + 8x + x2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + 8x + x2 = 37

Factor a perfect square on the left side:
(x + 4)(x + 4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + 4) equal to 6.08276253 and -6.08276253.

Subproblem 1
x + 4 = 6.08276253

Simplifying
x + 4 = 6.08276253

Reorder the terms:
4 + x = 6.08276253

Solving
4 + x = 6.08276253

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 6.08276253 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.08276253 + -4
x = 6.08276253 + -4

Combine like terms: 6.08276253 + -4 = 2.08276253
x = 2.08276253

Simplifying
x = 2.08276253

Subproblem 2
x + 4 = -6.08276253

Simplifying
x + 4 = -6.08276253

Reorder the terms:
4 + x = -6.08276253

Solving
4 + x = -6.08276253

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -6.08276253 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.08276253 + -4
x = -6.08276253 + -4

Combine like terms: -6.08276253 + -4 = -10.08276253
x = -10.08276253

Simplifying
x = -10.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.08276253, -10.08276253}