r^2+3r-72=0

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Solution for r^2+3r-72=0 equation:


Simplifying
r2 + 3r + -72 = 0

Reorder the terms:
-72 + 3r + r2 = 0

Solving
-72 + 3r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 3r + 72 + r2 = 0 + 72

Reorder the terms:
-72 + 72 + 3r + r2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 3r + r2 = 0 + 72
3r + r2 = 0 + 72

Combine like terms: 0 + 72 = 72
3r + r2 = 72

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 = 72 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 72 + 2.25

Combine like terms: 72 + 2.25 = 74.25
2.25 + 3r + r2 = 74.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(r + 1.5) equal to 8.61684397 and -8.61684397.

Subproblem 1

r + 1.5 = 8.61684397 Simplifying r + 1.5 = 8.61684397 Reorder the terms: 1.5 + r = 8.61684397 Solving 1.5 + r = 8.61684397 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 = 8.61684397 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 8.61684397 + -1.5 r = 8.61684397 + -1.5 Combine like terms: 8.61684397 + -1.5 = 7.11684397 r = 7.11684397 Simplifying r = 7.11684397

Subproblem 2

r + 1.5 = -8.61684397 Simplifying r + 1.5 = -8.61684397 Reorder the terms: 1.5 + r = -8.61684397 Solving 1.5 + r = -8.61684397 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 = -8.61684397 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -8.61684397 + -1.5 r = -8.61684397 + -1.5 Combine like terms: -8.61684397 + -1.5 = -10.11684397 r = -10.11684397 Simplifying r = -10.11684397

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.11684397, -10.11684397}

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