10x+20+x^2+2x+20x-50x-100=0

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Solution for 10x+20+x^2+2x+20x-50x-100=0 equation:


Simplifying
10x + 20 + x2 + 2x + 20x + -50x + -100 = 0

Reorder the terms:
20 + -100 + 10x + 2x + 20x + -50x + x2 = 0

Combine like terms: 20 + -100 = -80
-80 + 10x + 2x + 20x + -50x + x2 = 0

Combine like terms: 10x + 2x = 12x
-80 + 12x + 20x + -50x + x2 = 0

Combine like terms: 12x + 20x = 32x
-80 + 32x + -50x + x2 = 0

Combine like terms: 32x + -50x = -18x
-80 + -18x + x2 = 0

Solving
-80 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -18x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -18x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -18x + x2 = 0 + 80
-18x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-18x + x2 = 80

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 80 + 81

Reorder the terms:
81 + -18x + x2 = 80 + 81

Combine like terms: 80 + 81 = 161
81 + -18x + x2 = 161

Factor a perfect square on the left side:
(x + -9)(x + -9) = 161

Calculate the square root of the right side: 12.68857754

Break this problem into two subproblems by setting 
(x + -9) equal to 12.68857754 and -12.68857754.

Subproblem 1

x + -9 = 12.68857754 Simplifying x + -9 = 12.68857754 Reorder the terms: -9 + x = 12.68857754 Solving -9 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.68857754 + 9 x = 12.68857754 + 9 Combine like terms: 12.68857754 + 9 = 21.68857754 x = 21.68857754 Simplifying x = 21.68857754

Subproblem 2

x + -9 = -12.68857754 Simplifying x + -9 = -12.68857754 Reorder the terms: -9 + x = -12.68857754 Solving -9 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.68857754 + 9 x = -12.68857754 + 9 Combine like terms: -12.68857754 + 9 = -3.68857754 x = -3.68857754 Simplifying x = -3.68857754

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.68857754, -3.68857754}

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