5r^2-20=-r

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Solution for 5r^2-20=-r equation:


Simplifying
5r2 + -20 = -1r

Reorder the terms:
-20 + 5r2 = -1r

Solving
-20 + 5r2 = -1r

Solving for variable 'r'.

Reorder the terms:
-20 + r + 5r2 = -1r + r

Combine like terms: -1r + r = 0
-20 + r + 5r2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-4 + 0.2r + r2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.2r + 4 + r2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.2r + r2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.2r + r2 = 0 + 4
0.2r + r2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.2r + r2 = 4

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2r + 0.25 + r2 = 4 + 0.25

Reorder the terms:
0.25 + 0.2r + r2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + 0.2r + r2 = 4.25

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(r + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

r + 0.5 = 2.061552813 Simplifying r + 0.5 = 2.061552813 Reorder the terms: 0.5 + r = 2.061552813 Solving 0.5 + r = 2.061552813 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 2.061552813 + -0.5 r = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 r = 1.561552813 Simplifying r = 1.561552813

Subproblem 2

r + 0.5 = -2.061552813 Simplifying r + 0.5 = -2.061552813 Reorder the terms: 0.5 + r = -2.061552813 Solving 0.5 + r = -2.061552813 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -2.061552813 + -0.5 r = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 r = -2.561552813 Simplifying r = -2.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.561552813, -2.561552813}

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