x^2+20x-48=0

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Solution for x^2+20x-48=0 equation: 


Simplifying
x2 + 20x + -48 = 0

Reorder the terms:
-48 + 20x + x2 = 0

Solving
-48 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 20x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 20x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 20x + x2 = 0 + 48
20x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
20x + x2 = 48

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 48 + 100

Reorder the terms:
100 + 20x + x2 = 48 + 100

Combine like terms: 48 + 100 = 148
100 + 20x + x2 = 148

Factor a perfect square on the left side:
(x + 10)(x + 10) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + 10) equal to 12.165525061 and -12.165525061.


Subproblem 1
x + 10 = 12.165525061

Simplifying
x + 10 = 12.165525061

Reorder the terms:
10 + x = 12.165525061

Solving
10 + x = 12.165525061

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 12.165525061 + -10

Combine like terms: 10 + -10 = 0
0 + x = 12.165525061 + -10
x = 12.165525061 + -10

Combine like terms: 12.165525061 + -10 = 2.165525061
x = 2.165525061

Simplifying
x = 2.165525061


Subproblem 2
x + 10 = -12.165525061

Simplifying
x + 10 = -12.165525061

Reorder the terms:
10 + x = -12.165525061

Solving
10 + x = -12.165525061

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -12.165525061 + -10

Combine like terms: 10 + -10 = 0
0 + x = -12.165525061 + -10
x = -12.165525061 + -10

Combine like terms: -12.165525061 + -10 = -22.165525061
x = -22.165525061

Simplifying
x = -22.165525061


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.165525061, -22.165525061}

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