65+x(x-5)=180

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Solution for 65+x(x-5)=180 equation:


Simplifying
65 + x(x + -5) = 180

Reorder the terms:
65 + x(-5 + x) = 180
65 + (-5 * x + x * x) = 180
65 + (-5x + x2) = 180

Solving
65 + -5x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
65 + -180 + -5x + x2 = 180 + -180

Combine like terms: 65 + -180 = -115
-115 + -5x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-115 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '115' to each side of the equation.
-115 + -5x + 115 + x2 = 0 + 115

Reorder the terms:
-115 + 115 + -5x + x2 = 0 + 115

Combine like terms: -115 + 115 = 0
0 + -5x + x2 = 0 + 115
-5x + x2 = 0 + 115

Combine like terms: 0 + 115 = 115
-5x + x2 = 115

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 = 115 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 115 + 6.25

Combine like terms: 115 + 6.25 = 121.25
6.25 + -5x + x2 = 121.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 121.25

Calculate the square root of the right side: 11.011357773

Break this problem into two subproblems by setting 
(x + -2.5) equal to 11.011357773 and -11.011357773.

Subproblem 1

x + -2.5 = 11.011357773 Simplifying x + -2.5 = 11.011357773 Reorder the terms: -2.5 + x = 11.011357773 Solving -2.5 + x = 11.011357773 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 = 11.011357773 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 11.011357773 + 2.5 x = 11.011357773 + 2.5 Combine like terms: 11.011357773 + 2.5 = 13.511357773 x = 13.511357773 Simplifying x = 13.511357773

Subproblem 2

x + -2.5 = -11.011357773 Simplifying x + -2.5 = -11.011357773 Reorder the terms: -2.5 + x = -11.011357773 Solving -2.5 + x = -11.011357773 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 = -11.011357773 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -11.011357773 + 2.5 x = -11.011357773 + 2.5 Combine like terms: -11.011357773 + 2.5 = -8.511357773 x = -8.511357773 Simplifying x = -8.511357773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.511357773, -8.511357773}

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