x^2+30x+21=0

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Solution for x^2+30x+21=0 equation: 


Simplifying
x2 + 30x + 21 = 0

Reorder the terms:
21 + 30x + x2 = 0

Solving
21 + 30x + 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 + 30x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + 30x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 30x + x2 = 0 + -21
30x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
30x + x2 = -21

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -21 + 225

Reorder the terms:
225 + 30x + x2 = -21 + 225

Combine like terms: -21 + 225 = 204
225 + 30x + x2 = 204

Factor a perfect square on the left side:
(x + 15)(x + 15) = 204

Calculate the square root of the right side: 14.282856857

Break this problem into two subproblems by setting 
(x + 15) equal to 14.282856857 and -14.282856857.


Subproblem 1
x + 15 = 14.282856857

Simplifying
x + 15 = 14.282856857

Reorder the terms:
15 + x = 14.282856857

Solving
15 + x = 14.282856857

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 14.282856857 + -15

Combine like terms: 15 + -15 = 0
0 + x = 14.282856857 + -15
x = 14.282856857 + -15

Combine like terms: 14.282856857 + -15 = -0.717143143
x = -0.717143143

Simplifying
x = -0.717143143


Subproblem 2
x + 15 = -14.282856857

Simplifying
x + 15 = -14.282856857

Reorder the terms:
15 + x = -14.282856857

Solving
15 + x = -14.282856857

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -14.282856857 + -15

Combine like terms: 15 + -15 = 0
0 + x = -14.282856857 + -15
x = -14.282856857 + -15

Combine like terms: -14.282856857 + -15 = -29.282856857
x = -29.282856857

Simplifying
x = -29.282856857


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.717143143, -29.282856857}

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