x^2+20x=104

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Solution for x^2+20x=104 equation:


Simplifying
x2 + 20x = 104

Reorder the terms:
20x + x2 = 104

Solving
20x + x2 = 104

Solving for variable 'x'.

Reorder the terms:
-104 + 20x + x2 = 104 + -104

Combine like terms: 104 + -104 = 0
-104 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '104' to each side of the equation.
-104 + 20x + 104 + x2 = 0 + 104

Reorder the terms:
-104 + 104 + 20x + x2 = 0 + 104

Combine like terms: -104 + 104 = 0
0 + 20x + x2 = 0 + 104
20x + x2 = 0 + 104

Combine like terms: 0 + 104 = 104
20x + x2 = 104

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 = 104 + 100

Reorder the terms:
100 + 20x + x2 = 104 + 100

Combine like terms: 104 + 100 = 204
100 + 20x + x2 = 204

Factor a perfect square on the left side:
(x + 10)(x + 10) = 204

Calculate the square root of the right side: 14.282856857

Break this problem into two subproblems by setting 
(x + 10) equal to 14.282856857 and -14.282856857.

Subproblem 1

x + 10 = 14.282856857 Simplifying x + 10 = 14.282856857 Reorder the terms: 10 + x = 14.282856857 Solving 10 + x = 14.282856857 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 = 14.282856857 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.282856857 + -10 x = 14.282856857 + -10 Combine like terms: 14.282856857 + -10 = 4.282856857 x = 4.282856857 Simplifying x = 4.282856857

Subproblem 2

x + 10 = -14.282856857 Simplifying x + 10 = -14.282856857 Reorder the terms: 10 + x = -14.282856857 Solving 10 + x = -14.282856857 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 = -14.282856857 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.282856857 + -10 x = -14.282856857 + -10 Combine like terms: -14.282856857 + -10 = -24.282856857 x = -24.282856857 Simplifying x = -24.282856857

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.282856857, -24.282856857}

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