180=5x+x^2

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Solution for 180=5x+x^2 equation:


Simplifying
180 = 5x + x2

Solving
180 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
180 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
180 + -5x + -1x2 = 0 + x2 + -1x2
180 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
180 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-180 + 5x + x2 = 0

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 5x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 5x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 5x + x2 = 0 + 180
5x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
5x + x2 = 180

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 180 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 180 + 6.25

Combine like terms: 180 + 6.25 = 186.25
6.25 + 5x + x2 = 186.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 186.25

Calculate the square root of the right side: 13.647344064

Break this problem into two subproblems by setting 
(x + 2.5) equal to 13.647344064 and -13.647344064.

Subproblem 1

x + 2.5 = 13.647344064 Simplifying x + 2.5 = 13.647344064 Reorder the terms: 2.5 + x = 13.647344064 Solving 2.5 + x = 13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.647344064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.647344064 + -2.5 x = 13.647344064 + -2.5 Combine like terms: 13.647344064 + -2.5 = 11.147344064 x = 11.147344064 Simplifying x = 11.147344064

Subproblem 2

x + 2.5 = -13.647344064 Simplifying x + 2.5 = -13.647344064 Reorder the terms: 2.5 + x = -13.647344064 Solving 2.5 + x = -13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.647344064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.647344064 + -2.5 x = -13.647344064 + -2.5 Combine like terms: -13.647344064 + -2.5 = -16.147344064 x = -16.147344064 Simplifying x = -16.147344064

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.147344064, -16.147344064}

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