r^2-10r-400=0

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Solution for r^2-10r-400=0 equation:


Simplifying
r2 + -10r + -400 = 0

Reorder the terms:
-400 + -10r + r2 = 0

Solving
-400 + -10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -10r + 400 + r2 = 0 + 400

Reorder the terms:
-400 + 400 + -10r + r2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -10r + r2 = 0 + 400
-10r + r2 = 0 + 400

Combine like terms: 0 + 400 = 400
-10r + r2 = 400

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 = 400 + 25

Reorder the terms:
25 + -10r + r2 = 400 + 25

Combine like terms: 400 + 25 = 425
25 + -10r + r2 = 425

Factor a perfect square on the left side:
(r + -5)(r + -5) = 425

Calculate the square root of the right side: 20.615528128

Break this problem into two subproblems by setting 
(r + -5) equal to 20.615528128 and -20.615528128.

Subproblem 1

r + -5 = 20.615528128 Simplifying r + -5 = 20.615528128 Reorder the terms: -5 + r = 20.615528128 Solving -5 + r = 20.615528128 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 = 20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + r = 20.615528128 + 5 r = 20.615528128 + 5 Combine like terms: 20.615528128 + 5 = 25.615528128 r = 25.615528128 Simplifying r = 25.615528128

Subproblem 2

r + -5 = -20.615528128 Simplifying r + -5 = -20.615528128 Reorder the terms: -5 + r = -20.615528128 Solving -5 + r = -20.615528128 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 = -20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + r = -20.615528128 + 5 r = -20.615528128 + 5 Combine like terms: -20.615528128 + 5 = -15.615528128 r = -15.615528128 Simplifying r = -15.615528128

Solution

The solution to the problem is based on the solutions from the subproblems. r = {25.615528128, -15.615528128}

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