x^2+48x-40=0

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Solution for x^2+48x-40=0 equation: 


Simplifying
x2 + 48x + -40 = 0

Reorder the terms:
-40 + 48x + x2 = 0

Solving
-40 + 48x + 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 + 48x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 48x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 48x + x2 = 0 + 40
48x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
48x + x2 = 40

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 = 40 + 576

Reorder the terms:
576 + 48x + x2 = 40 + 576

Combine like terms: 40 + 576 = 616
576 + 48x + x2 = 616

Factor a perfect square on the left side:
(x + 24)(x + 24) = 616

Calculate the square root of the right side: 24.819347292

Break this problem into two subproblems by setting 
(x + 24) equal to 24.819347292 and -24.819347292.


Subproblem 1
x + 24 = 24.819347292

Simplifying
x + 24 = 24.819347292

Reorder the terms:
24 + x = 24.819347292

Solving
24 + x = 24.819347292

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 = 24.819347292 + -24

Combine like terms: 24 + -24 = 0
0 + x = 24.819347292 + -24
x = 24.819347292 + -24

Combine like terms: 24.819347292 + -24 = 0.819347292
x = 0.819347292

Simplifying
x = 0.819347292


Subproblem 2
x + 24 = -24.819347292

Simplifying
x + 24 = -24.819347292

Reorder the terms:
24 + x = -24.819347292

Solving
24 + x = -24.819347292

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 = -24.819347292 + -24

Combine like terms: 24 + -24 = 0
0 + x = -24.819347292 + -24
x = -24.819347292 + -24

Combine like terms: -24.819347292 + -24 = -48.819347292
x = -48.819347292

Simplifying
x = -48.819347292


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.819347292, -48.819347292}

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