x^2+30x-336=0

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Solution for x^2+30x-336=0 equation: 


Simplifying
x2 + 30x + -336 = 0

Reorder the terms:
-336 + 30x + x2 = 0

Solving
-336 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '336' to each side of the equation.
-336 + 30x + 336 + x2 = 0 + 336

Reorder the terms:
-336 + 336 + 30x + x2 = 0 + 336

Combine like terms: -336 + 336 = 0
0 + 30x + x2 = 0 + 336
30x + x2 = 0 + 336

Combine like terms: 0 + 336 = 336
30x + x2 = 336

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 = 336 + 225

Reorder the terms:
225 + 30x + x2 = 336 + 225

Combine like terms: 336 + 225 = 561
225 + 30x + x2 = 561

Factor a perfect square on the left side:
(x + 15)(x + 15) = 561

Calculate the square root of the right side: 23.685438565

Break this problem into two subproblems by setting 
(x + 15) equal to 23.685438565 and -23.685438565.


Subproblem 1
x + 15 = 23.685438565

Simplifying
x + 15 = 23.685438565

Reorder the terms:
15 + x = 23.685438565

Solving
15 + x = 23.685438565

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 = 23.685438565 + -15

Combine like terms: 15 + -15 = 0
0 + x = 23.685438565 + -15
x = 23.685438565 + -15

Combine like terms: 23.685438565 + -15 = 8.685438565
x = 8.685438565

Simplifying
x = 8.685438565


Subproblem 2
x + 15 = -23.685438565

Simplifying
x + 15 = -23.685438565

Reorder the terms:
15 + x = -23.685438565

Solving
15 + x = -23.685438565

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 = -23.685438565 + -15

Combine like terms: 15 + -15 = 0
0 + x = -23.685438565 + -15
x = -23.685438565 + -15

Combine like terms: -23.685438565 + -15 = -38.685438565
x = -38.685438565

Simplifying
x = -38.685438565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.685438565, -38.685438565}

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