r^2-10r-225=0

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Solution for r^2-10r-225=0 equation:


Simplifying
r2 + -10r + -225 = 0

Reorder the terms:
-225 + -10r + r2 = 0

Solving
-225 + -10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -10r + 225 + r2 = 0 + 225

Reorder the terms:
-225 + 225 + -10r + r2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -10r + r2 = 0 + 225
-10r + r2 = 0 + 225

Combine like terms: 0 + 225 = 225
-10r + r2 = 225

The r term is -10r.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r + 25 + r2 = 225 + 25

Reorder the terms:
25 + -10r + r2 = 225 + 25

Combine like terms: 225 + 25 = 250
25 + -10r + r2 = 250

Factor a perfect square on the left side:
(r + -5)(r + -5) = 250

Calculate the square root of the right side: 15.811388301

Break this problem into two subproblems by setting 
(r + -5) equal to 15.811388301 and -15.811388301.

Subproblem 1

r + -5 = 15.811388301 Simplifying r + -5 = 15.811388301 Reorder the terms: -5 + r = 15.811388301 Solving -5 + r = 15.811388301 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 15.811388301 + 5 Combine like terms: -5 + 5 = 0 0 + r = 15.811388301 + 5 r = 15.811388301 + 5 Combine like terms: 15.811388301 + 5 = 20.811388301 r = 20.811388301 Simplifying r = 20.811388301

Subproblem 2

r + -5 = -15.811388301 Simplifying r + -5 = -15.811388301 Reorder the terms: -5 + r = -15.811388301 Solving -5 + r = -15.811388301 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -15.811388301 + 5 Combine like terms: -5 + 5 = 0 0 + r = -15.811388301 + 5 r = -15.811388301 + 5 Combine like terms: -15.811388301 + 5 = -10.811388301 r = -10.811388301 Simplifying r = -10.811388301

Solution

The solution to the problem is based on the solutions from the subproblems. r = {20.811388301, -10.811388301}

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