2x+120+x^2-x=180

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Solution for 2x+120+x^2-x=180 equation:


Simplifying
2x + 120 + x2 + -1x = 180

Reorder the terms:
120 + 2x + -1x + x2 = 180

Combine like terms: 2x + -1x = 1x
120 + 1x + x2 = 180

Solving
120 + 1x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
120 + -180 + 1x + x2 = 180 + -180

Combine like terms: 120 + -180 = -60
-60 + 1x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-60 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 1x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 1x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 1x + x2 = 0 + 60
1x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
1x + x2 = 60

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 60 + 0.25

Reorder the terms:
0.25 + x + x2 = 60 + 0.25

Combine like terms: 60 + 0.25 = 60.25
0.25 + x + x2 = 60.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

x + 0.5 = 7.762087348 Simplifying x + 0.5 = 7.762087348 Reorder the terms: 0.5 + x = 7.762087348 Solving 0.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.762087348 + -0.5 x = 7.762087348 + -0.5 Combine like terms: 7.762087348 + -0.5 = 7.262087348 x = 7.262087348 Simplifying x = 7.262087348

Subproblem 2

x + 0.5 = -7.762087348 Simplifying x + 0.5 = -7.762087348 Reorder the terms: 0.5 + x = -7.762087348 Solving 0.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.762087348 + -0.5 x = -7.762087348 + -0.5 Combine like terms: -7.762087348 + -0.5 = -8.262087348 x = -8.262087348 Simplifying x = -8.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.262087348, -8.262087348}

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