x^2+20x-50=0

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Solution for x^2+20x-50=0 equation:


Simplifying
x2 + 20x + -50 = 0

Reorder the terms:
-50 + 20x + x2 = 0

Solving
-50 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 20x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 20x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 20x + x2 = 0 + 50
20x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
20x + x2 = 50

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 = 50 + 100

Reorder the terms:
100 + 20x + x2 = 50 + 100

Combine like terms: 50 + 100 = 150
100 + 20x + x2 = 150

Factor a perfect square on the left side:
(x + 10)(x + 10) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(x + 10) equal to 12.247448714 and -12.247448714.

Subproblem 1

x + 10 = 12.247448714 Simplifying x + 10 = 12.247448714 Reorder the terms: 10 + x = 12.247448714 Solving 10 + x = 12.247448714 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 = 12.247448714 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.247448714 + -10 x = 12.247448714 + -10 Combine like terms: 12.247448714 + -10 = 2.247448714 x = 2.247448714 Simplifying x = 2.247448714

Subproblem 2

x + 10 = -12.247448714 Simplifying x + 10 = -12.247448714 Reorder the terms: 10 + x = -12.247448714 Solving 10 + x = -12.247448714 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 = -12.247448714 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.247448714 + -10 x = -12.247448714 + -10 Combine like terms: -12.247448714 + -10 = -22.247448714 x = -22.247448714 Simplifying x = -22.247448714

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.247448714, -22.247448714}

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