x^2+48x-128=0

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Solution for x^2+48x-128=0 equation: 


Simplifying
x2 + 48x + -128 = 0

Reorder the terms:
-128 + 48x + x2 = 0

Solving
-128 + 48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + 48x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + 48x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 48x + x2 = 0 + 128
48x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
48x + x2 = 128

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = 128 + 576

Reorder the terms:
576 + 48x + x2 = 128 + 576

Combine like terms: 128 + 576 = 704
576 + 48x + x2 = 704

Factor a perfect square on the left side:
(x + 24)(x + 24) = 704

Calculate the square root of the right side: 26.532998323

Break this problem into two subproblems by setting 
(x + 24) equal to 26.532998323 and -26.532998323.


Subproblem 1
x + 24 = 26.532998323

Simplifying
x + 24 = 26.532998323

Reorder the terms:
24 + x = 26.532998323

Solving
24 + x = 26.532998323

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = 26.532998323 + -24

Combine like terms: 24 + -24 = 0
0 + x = 26.532998323 + -24
x = 26.532998323 + -24

Combine like terms: 26.532998323 + -24 = 2.532998323
x = 2.532998323

Simplifying
x = 2.532998323


Subproblem 2
x + 24 = -26.532998323

Simplifying
x + 24 = -26.532998323

Reorder the terms:
24 + x = -26.532998323

Solving
24 + x = -26.532998323

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = -26.532998323 + -24

Combine like terms: 24 + -24 = 0
0 + x = -26.532998323 + -24
x = -26.532998323 + -24

Combine like terms: -26.532998323 + -24 = -50.532998323
x = -50.532998323

Simplifying
x = -50.532998323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.532998323, -50.532998323}

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