x^2+20x-47=0

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Solution for x^2+20x-47=0 equation: 


Simplifying
x2 + 20x + -47 = 0

Reorder the terms:
-47 + 20x + x2 = 0

Solving
-47 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + 20x + 47 + x2 = 0 + 47

Reorder the terms:
-47 + 47 + 20x + x2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 20x + x2 = 0 + 47
20x + x2 = 0 + 47

Combine like terms: 0 + 47 = 47
20x + x2 = 47

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 = 47 + 100

Reorder the terms:
100 + 20x + x2 = 47 + 100

Combine like terms: 47 + 100 = 147
100 + 20x + x2 = 147

Factor a perfect square on the left side:
(x + 10)(x + 10) = 147

Calculate the square root of the right side: 12.124355653

Break this problem into two subproblems by setting 
(x + 10) equal to 12.124355653 and -12.124355653.


Subproblem 1
x + 10 = 12.124355653

Simplifying
x + 10 = 12.124355653

Reorder the terms:
10 + x = 12.124355653

Solving
10 + x = 12.124355653

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 = 12.124355653 + -10

Combine like terms: 10 + -10 = 0
0 + x = 12.124355653 + -10
x = 12.124355653 + -10

Combine like terms: 12.124355653 + -10 = 2.124355653
x = 2.124355653

Simplifying
x = 2.124355653


Subproblem 2
x + 10 = -12.124355653

Simplifying
x + 10 = -12.124355653

Reorder the terms:
10 + x = -12.124355653

Solving
10 + x = -12.124355653

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 = -12.124355653 + -10

Combine like terms: 10 + -10 = 0
0 + x = -12.124355653 + -10
x = -12.124355653 + -10

Combine like terms: -12.124355653 + -10 = -22.124355653
x = -22.124355653

Simplifying
x = -22.124355653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.124355653, -22.124355653}

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