x(x+20)=84

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Solution for x(x+20)=84 equation: 


Simplifying
x(x + 20) = 84

Reorder the terms:
x(20 + x) = 84
(20 * x + x * x) = 84
(20x + x2) = 84

Solving
20x + x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + 20x + x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 20x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 20x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 20x + x2 = 0 + 84
20x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
20x + x2 = 84

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 = 84 + 100

Reorder the terms:
100 + 20x + x2 = 84 + 100

Combine like terms: 84 + 100 = 184
100 + 20x + x2 = 184

Factor a perfect square on the left side:
(x + 10)(x + 10) = 184

Calculate the square root of the right side: 13.564659966

Break this problem into two subproblems by setting 
(x + 10) equal to 13.564659966 and -13.564659966.


Subproblem 1
x + 10 = 13.564659966

Simplifying
x + 10 = 13.564659966

Reorder the terms:
10 + x = 13.564659966

Solving
10 + x = 13.564659966

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 = 13.564659966 + -10

Combine like terms: 10 + -10 = 0
0 + x = 13.564659966 + -10
x = 13.564659966 + -10

Combine like terms: 13.564659966 + -10 = 3.564659966
x = 3.564659966

Simplifying
x = 3.564659966


Subproblem 2
x + 10 = -13.564659966

Simplifying
x + 10 = -13.564659966

Reorder the terms:
10 + x = -13.564659966

Solving
10 + x = -13.564659966

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 = -13.564659966 + -10

Combine like terms: 10 + -10 = 0
0 + x = -13.564659966 + -10
x = -13.564659966 + -10

Combine like terms: -13.564659966 + -10 = -23.564659966
x = -23.564659966

Simplifying
x = -23.564659966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.564659966, -23.564659966}

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