120x=(x+2)(120-x)

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Solution for 120x=(x+2)(120-x) equation:


Simplifying
120x = (x + 2)(120 + -1x)

Reorder the terms:
120x = (2 + x)(120 + -1x)

Multiply (2 + x) * (120 + -1x)
120x = (2(120 + -1x) + x(120 + -1x))
120x = ((120 * 2 + -1x * 2) + x(120 + -1x))
120x = ((240 + -2x) + x(120 + -1x))
120x = (240 + -2x + (120 * x + -1x * x))
120x = (240 + -2x + (120x + -1x2))

Combine like terms: -2x + 120x = 118x
120x = (240 + 118x + -1x2)

Solving
120x = 240 + 118x + -1x2

Solving for variable 'x'.

Reorder the terms:
-240 + 120x + -118x + x2 = 240 + 118x + -1x2 + -240 + -118x + x2

Combine like terms: 120x + -118x = 2x
-240 + 2x + x2 = 240 + 118x + -1x2 + -240 + -118x + x2

Reorder the terms:
-240 + 2x + x2 = 240 + -240 + 118x + -118x + -1x2 + x2

Combine like terms: 240 + -240 = 0
-240 + 2x + x2 = 0 + 118x + -118x + -1x2 + x2
-240 + 2x + x2 = 118x + -118x + -1x2 + x2

Combine like terms: 118x + -118x = 0
-240 + 2x + x2 = 0 + -1x2 + x2
-240 + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-240 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + 2x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + 2x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + 2x + x2 = 0 + 240
2x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
2x + x2 = 240

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 240 + 1

Reorder the terms:
1 + 2x + x2 = 240 + 1

Combine like terms: 240 + 1 = 241
1 + 2x + x2 = 241

Factor a perfect square on the left side:
(x + 1)(x + 1) = 241

Calculate the square root of the right side: 15.524174696

Break this problem into two subproblems by setting 
(x + 1) equal to 15.524174696 and -15.524174696.

Subproblem 1

x + 1 = 15.524174696 Simplifying x + 1 = 15.524174696 Reorder the terms: 1 + x = 15.524174696 Solving 1 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 15.524174696 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.524174696 + -1 x = 15.524174696 + -1 Combine like terms: 15.524174696 + -1 = 14.524174696 x = 14.524174696 Simplifying x = 14.524174696

Subproblem 2

x + 1 = -15.524174696 Simplifying x + 1 = -15.524174696 Reorder the terms: 1 + x = -15.524174696 Solving 1 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -15.524174696 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.524174696 + -1 x = -15.524174696 + -1 Combine like terms: -15.524174696 + -1 = -16.524174696 x = -16.524174696 Simplifying x = -16.524174696

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.524174696, -16.524174696}

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