x^2+30x+40=0

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Solution for x^2+30x+40=0 equation: 


Simplifying
x2 + 30x + 40 = 0

Reorder the terms:
40 + 30x + x2 = 0

Solving
40 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 30x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 30x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 30x + x2 = 0 + -40
30x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
30x + x2 = -40

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 = -40 + 225

Reorder the terms:
225 + 30x + x2 = -40 + 225

Combine like terms: -40 + 225 = 185
225 + 30x + x2 = 185

Factor a perfect square on the left side:
(x + 15)(x + 15) = 185

Calculate the square root of the right side: 13.601470509

Break this problem into two subproblems by setting 
(x + 15) equal to 13.601470509 and -13.601470509.


Subproblem 1
x + 15 = 13.601470509

Simplifying
x + 15 = 13.601470509

Reorder the terms:
15 + x = 13.601470509

Solving
15 + x = 13.601470509

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 = 13.601470509 + -15

Combine like terms: 15 + -15 = 0
0 + x = 13.601470509 + -15
x = 13.601470509 + -15

Combine like terms: 13.601470509 + -15 = -1.398529491
x = -1.398529491

Simplifying
x = -1.398529491


Subproblem 2
x + 15 = -13.601470509

Simplifying
x + 15 = -13.601470509

Reorder the terms:
15 + x = -13.601470509

Solving
15 + x = -13.601470509

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 = -13.601470509 + -15

Combine like terms: 15 + -15 = 0
0 + x = -13.601470509 + -15
x = -13.601470509 + -15

Combine like terms: -13.601470509 + -15 = -28.601470509
x = -28.601470509

Simplifying
x = -28.601470509


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.398529491, -28.601470509}

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