r^2+3r=32400

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Solution for r^2+3r=32400 equation:


Simplifying
r2 + 3r = 32400

Reorder the terms:
3r + r2 = 32400

Solving
3r + r2 = 32400

Solving for variable 'r'.

Reorder the terms:
-32400 + 3r + r2 = 32400 + -32400

Combine like terms: 32400 + -32400 = 0
-32400 + 3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32400' to each side of the equation.
-32400 + 3r + 32400 + r2 = 0 + 32400

Reorder the terms:
-32400 + 32400 + 3r + r2 = 0 + 32400

Combine like terms: -32400 + 32400 = 0
0 + 3r + r2 = 0 + 32400
3r + r2 = 0 + 32400

Combine like terms: 0 + 32400 = 32400
3r + r2 = 32400

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 32400 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 32400 + 2.25

Combine like terms: 32400 + 2.25 = 32402.25
2.25 + 3r + r2 = 32402.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 32402.25

Calculate the square root of the right side: 180.006249891

Break this problem into two subproblems by setting 
(r + 1.5) equal to 180.006249891 and -180.006249891.

Subproblem 1

r + 1.5 = 180.006249891 Simplifying r + 1.5 = 180.006249891 Reorder the terms: 1.5 + r = 180.006249891 Solving 1.5 + r = 180.006249891 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = 180.006249891 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 180.006249891 + -1.5 r = 180.006249891 + -1.5 Combine like terms: 180.006249891 + -1.5 = 178.506249891 r = 178.506249891 Simplifying r = 178.506249891

Subproblem 2

r + 1.5 = -180.006249891 Simplifying r + 1.5 = -180.006249891 Reorder the terms: 1.5 + r = -180.006249891 Solving 1.5 + r = -180.006249891 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = -180.006249891 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -180.006249891 + -1.5 r = -180.006249891 + -1.5 Combine like terms: -180.006249891 + -1.5 = -181.506249891 r = -181.506249891 Simplifying r = -181.506249891

Solution

The solution to the problem is based on the solutions from the subproblems. r = {178.506249891, -181.506249891}

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