x^2+20x+1=0

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Solution for x^2+20x+1=0 equation:


Simplifying
x2 + 20x + 1 = 0

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

Solving
1 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 20x + -1 + x2 = 0 + -1

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

Combine like terms: 1 + -1 = 0
0 + 20x + x2 = 0 + -1
20x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
20x + x2 = -1

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 = -1 + 100

Reorder the terms:
100 + 20x + x2 = -1 + 100

Combine like terms: -1 + 100 = 99
100 + 20x + x2 = 99

Factor a perfect square on the left side:
(x + 10)(x + 10) = 99

Calculate the square root of the right side: 9.949874371

Break this problem into two subproblems by setting 
(x + 10) equal to 9.949874371 and -9.949874371.

Subproblem 1

x + 10 = 9.949874371 Simplifying x + 10 = 9.949874371 Reorder the terms: 10 + x = 9.949874371 Solving 10 + x = 9.949874371 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 = 9.949874371 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.949874371 + -10 x = 9.949874371 + -10 Combine like terms: 9.949874371 + -10 = -0.050125629 x = -0.050125629 Simplifying x = -0.050125629

Subproblem 2

x + 10 = -9.949874371 Simplifying x + 10 = -9.949874371 Reorder the terms: 10 + x = -9.949874371 Solving 10 + x = -9.949874371 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 = -9.949874371 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.949874371 + -10 x = -9.949874371 + -10 Combine like terms: -9.949874371 + -10 = -19.949874371 x = -19.949874371 Simplifying x = -19.949874371

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.050125629, -19.949874371}

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