x^2+20x-9=0

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Solution for x^2+20x-9=0 equation:


Simplifying
x2 + 20x + -9 = 0

Reorder the terms:
-9 + 20x + x2 = 0

Solving
-9 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 20x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 20x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 20x + x2 = 0 + 9
20x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
20x + x2 = 9

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 = 9 + 100

Reorder the terms:
100 + 20x + x2 = 9 + 100

Combine like terms: 9 + 100 = 109
100 + 20x + x2 = 109

Factor a perfect square on the left side:
(x + 10)(x + 10) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(x + 10) equal to 10.440306509 and -10.440306509.

Subproblem 1

x + 10 = 10.440306509 Simplifying x + 10 = 10.440306509 Reorder the terms: 10 + x = 10.440306509 Solving 10 + x = 10.440306509 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 = 10.440306509 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.440306509 + -10 x = 10.440306509 + -10 Combine like terms: 10.440306509 + -10 = 0.440306509 x = 0.440306509 Simplifying x = 0.440306509

Subproblem 2

x + 10 = -10.440306509 Simplifying x + 10 = -10.440306509 Reorder the terms: 10 + x = -10.440306509 Solving 10 + x = -10.440306509 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 = -10.440306509 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.440306509 + -10 x = -10.440306509 + -10 Combine like terms: -10.440306509 + -10 = -20.440306509 x = -20.440306509 Simplifying x = -20.440306509

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.440306509, -20.440306509}

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