r^2+18.5r-4=0

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Solution for r^2+18.5r-4=0 equation:


Simplifying
r2 + 18.5r + -4 = 0

Reorder the terms:
-4 + 18.5r + r2 = 0

Solving
-4 + 18.5r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 18.5r + 4 + r2 = 0 + 4

Reorder the terms:
-4 + 4 + 18.5r + r2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 18.5r + r2 = 0 + 4
18.5r + r2 = 0 + 4

Combine like terms: 0 + 4 = 4
18.5r + r2 = 4

The r term is 18.5r.  Take half its coefficient (9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
18.5r + 85.5625 + r2 = 4 + 85.5625

Reorder the terms:
85.5625 + 18.5r + r2 = 4 + 85.5625

Combine like terms: 4 + 85.5625 = 89.5625
85.5625 + 18.5r + r2 = 89.5625

Factor a perfect square on the left side:
(r + 9.25)(r + 9.25) = 89.5625

Calculate the square root of the right side: 9.463746615

Break this problem into two subproblems by setting 
(r + 9.25) equal to 9.463746615 and -9.463746615.

Subproblem 1

r + 9.25 = 9.463746615 Simplifying r + 9.25 = 9.463746615 Reorder the terms: 9.25 + r = 9.463746615 Solving 9.25 + r = 9.463746615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + r = 9.463746615 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + r = 9.463746615 + -9.25 r = 9.463746615 + -9.25 Combine like terms: 9.463746615 + -9.25 = 0.213746615 r = 0.213746615 Simplifying r = 0.213746615

Subproblem 2

r + 9.25 = -9.463746615 Simplifying r + 9.25 = -9.463746615 Reorder the terms: 9.25 + r = -9.463746615 Solving 9.25 + r = -9.463746615 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + r = -9.463746615 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + r = -9.463746615 + -9.25 r = -9.463746615 + -9.25 Combine like terms: -9.463746615 + -9.25 = -18.713746615 r = -18.713746615 Simplifying r = -18.713746615

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.213746615, -18.713746615}

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