r^2+15r-500=0

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Solution for r^2+15r-500=0 equation:


Simplifying
r2 + 15r + -500 = 0

Reorder the terms:
-500 + 15r + r2 = 0

Solving
-500 + 15r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 15r + 500 + r2 = 0 + 500

Reorder the terms:
-500 + 500 + 15r + r2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 15r + r2 = 0 + 500
15r + r2 = 0 + 500

Combine like terms: 0 + 500 = 500
15r + r2 = 500

The r term is 15r.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15r + 56.25 + r2 = 500 + 56.25

Reorder the terms:
56.25 + 15r + r2 = 500 + 56.25

Combine like terms: 500 + 56.25 = 556.25
56.25 + 15r + r2 = 556.25

Factor a perfect square on the left side:
(r + 7.5)(r + 7.5) = 556.25

Calculate the square root of the right side: 23.58495283

Break this problem into two subproblems by setting 
(r + 7.5) equal to 23.58495283 and -23.58495283.

Subproblem 1

r + 7.5 = 23.58495283 Simplifying r + 7.5 = 23.58495283 Reorder the terms: 7.5 + r = 23.58495283 Solving 7.5 + r = 23.58495283 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = 23.58495283 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = 23.58495283 + -7.5 r = 23.58495283 + -7.5 Combine like terms: 23.58495283 + -7.5 = 16.08495283 r = 16.08495283 Simplifying r = 16.08495283

Subproblem 2

r + 7.5 = -23.58495283 Simplifying r + 7.5 = -23.58495283 Reorder the terms: 7.5 + r = -23.58495283 Solving 7.5 + r = -23.58495283 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = -23.58495283 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = -23.58495283 + -7.5 r = -23.58495283 + -7.5 Combine like terms: -23.58495283 + -7.5 = -31.08495283 r = -31.08495283 Simplifying r = -31.08495283

Solution

The solution to the problem is based on the solutions from the subproblems. r = {16.08495283, -31.08495283}

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