x^2+20x-2=0

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


Simplifying
x2 + 20x + -2 = 0

Reorder the terms:
-2 + 20x + x2 = 0

Solving
-2 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 20x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 20x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 20x + x2 = 0 + 2
20x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
20x + x2 = 2

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 = 2 + 100

Reorder the terms:
100 + 20x + x2 = 2 + 100

Combine like terms: 2 + 100 = 102
100 + 20x + x2 = 102

Factor a perfect square on the left side:
(x + 10)(x + 10) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + 10) equal to 10.099504938 and -10.099504938.

Subproblem 1

x + 10 = 10.099504938 Simplifying x + 10 = 10.099504938 Reorder the terms: 10 + x = 10.099504938 Solving 10 + x = 10.099504938 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 = 10.099504938 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.099504938 + -10 x = 10.099504938 + -10 Combine like terms: 10.099504938 + -10 = 0.099504938 x = 0.099504938 Simplifying x = 0.099504938

Subproblem 2

x + 10 = -10.099504938 Simplifying x + 10 = -10.099504938 Reorder the terms: 10 + x = -10.099504938 Solving 10 + x = -10.099504938 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 = -10.099504938 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.099504938 + -10 x = -10.099504938 + -10 Combine like terms: -10.099504938 + -10 = -20.099504938 x = -20.099504938 Simplifying x = -20.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.099504938, -20.099504938}

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