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 = 50
100 + 20x + x2 = 50

Factor a perfect square on the left side:
(x + 10)(x + 10) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + 10) equal to 7.071067812 and -7.071067812.

Subproblem 1

x + 10 = 7.071067812 Simplifying x + 10 = 7.071067812 Reorder the terms: 10 + x = 7.071067812 Solving 10 + x = 7.071067812 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 = 7.071067812 + -10 Combine like terms: 10 + -10 = 0 0 + x = 7.071067812 + -10 x = 7.071067812 + -10 Combine like terms: 7.071067812 + -10 = -2.928932188 x = -2.928932188 Simplifying x = -2.928932188

Subproblem 2

x + 10 = -7.071067812 Simplifying x + 10 = -7.071067812 Reorder the terms: 10 + x = -7.071067812 Solving 10 + x = -7.071067812 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 = -7.071067812 + -10 Combine like terms: 10 + -10 = 0 0 + x = -7.071067812 + -10 x = -7.071067812 + -10 Combine like terms: -7.071067812 + -10 = -17.071067812 x = -17.071067812 Simplifying x = -17.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.928932188, -17.071067812}

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