X^2+2X=20

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Solution for X^2+2X=20 equation:


Simplifying
X2 + 2X = 20

Reorder the terms:
2X + X2 = 20

Solving
2X + X2 = 20

Solving for variable 'X'.

Reorder the terms:
-20 + 2X + X2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 2X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 2X + 20 + X2 = 0 + 20

Reorder the terms:
-20 + 20 + 2X + X2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 2X + X2 = 0 + 20
2X + X2 = 0 + 20

Combine like terms: 0 + 20 = 20
2X + X2 = 20

The X term is 2X.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2X + 1 + X2 = 20 + 1

Reorder the terms:
1 + 2X + X2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + 2X + X2 = 21

Factor a perfect square on the left side:
(X + 1)(X + 1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(X + 1) equal to 4.582575695 and -4.582575695.

Subproblem 1

X + 1 = 4.582575695 Simplifying X + 1 = 4.582575695 Reorder the terms: 1 + X = 4.582575695 Solving 1 + X = 4.582575695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + X = 4.582575695 + -1 X = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 X = 3.582575695 Simplifying X = 3.582575695

Subproblem 2

X + 1 = -4.582575695 Simplifying X + 1 = -4.582575695 Reorder the terms: 1 + X = -4.582575695 Solving 1 + X = -4.582575695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + X = -4.582575695 + -1 X = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 X = -5.582575695 Simplifying X = -5.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. X = {3.582575695, -5.582575695}

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