-x^2+20x+40=0

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Solution for -x^2+20x+40=0 equation: 


Simplifying
-1x2 + 20x + 40 = 0

Reorder the terms:
40 + 20x + -1x2 = 0

Solving
40 + 20x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-40 + -20x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -20x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -20x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -20x + x2 = 0 + 40
-20x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-20x + x2 = 40

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 = 40 + 100

Reorder the terms:
100 + -20x + x2 = 40 + 100

Combine like terms: 40 + 100 = 140
100 + -20x + x2 = 140

Factor a perfect square on the left side:
(x + -10)(x + -10) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(x + -10) equal to 11.832159566 and -11.832159566.


Subproblem 1
x + -10 = 11.832159566

Simplifying
x + -10 = 11.832159566

Reorder the terms:
-10 + x = 11.832159566

Solving
-10 + x = 11.832159566

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 = 11.832159566 + 10

Combine like terms: -10 + 10 = 0
0 + x = 11.832159566 + 10
x = 11.832159566 + 10

Combine like terms: 11.832159566 + 10 = 21.832159566
x = 21.832159566

Simplifying
x = 21.832159566


Subproblem 2
x + -10 = -11.832159566

Simplifying
x + -10 = -11.832159566

Reorder the terms:
-10 + x = -11.832159566

Solving
-10 + x = -11.832159566

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 = -11.832159566 + 10

Combine like terms: -10 + 10 = 0
0 + x = -11.832159566 + 10
x = -11.832159566 + 10

Combine like terms: -11.832159566 + 10 = -1.832159566
x = -1.832159566

Simplifying
x = -1.832159566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.832159566, -1.832159566}

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