x^2+32x+49=0

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Solution for x^2+32x+49=0 equation: 


Simplifying
x2 + 32x + 49 = 0

Reorder the terms:
49 + 32x + x2 = 0

Solving
49 + 32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 32x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + 32x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 32x + x2 = 0 + -49
32x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
32x + x2 = -49

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = -49 + 256

Reorder the terms:
256 + 32x + x2 = -49 + 256

Combine like terms: -49 + 256 = 207
256 + 32x + x2 = 207

Factor a perfect square on the left side:
(x + 16)(x + 16) = 207

Calculate the square root of the right side: 14.38749457

Break this problem into two subproblems by setting 
(x + 16) equal to 14.38749457 and -14.38749457.


Subproblem 1
x + 16 = 14.38749457

Simplifying
x + 16 = 14.38749457

Reorder the terms:
16 + x = 14.38749457

Solving
16 + x = 14.38749457

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = 14.38749457 + -16

Combine like terms: 16 + -16 = 0
0 + x = 14.38749457 + -16
x = 14.38749457 + -16

Combine like terms: 14.38749457 + -16 = -1.61250543
x = -1.61250543

Simplifying
x = -1.61250543


Subproblem 2
x + 16 = -14.38749457

Simplifying
x + 16 = -14.38749457

Reorder the terms:
16 + x = -14.38749457

Solving
16 + x = -14.38749457

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = -14.38749457 + -16

Combine like terms: 16 + -16 = 0
0 + x = -14.38749457 + -16
x = -14.38749457 + -16

Combine like terms: -14.38749457 + -16 = -30.38749457
x = -30.38749457

Simplifying
x = -30.38749457


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.61250543, -30.38749457}

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