20=3r^2+5r

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Solution for 20=3r^2+5r equation:


Simplifying
20 = 3r2 + 5r

Reorder the terms:
20 = 5r + 3r2

Solving
20 = 5r + 3r2

Solving for variable 'r'.

Reorder the terms:
20 + -5r + -3r2 = 5r + -5r + 3r2 + -3r2

Combine like terms: 5r + -5r = 0
20 + -5r + -3r2 = 0 + 3r2 + -3r2
20 + -5r + -3r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
20 + -5r + -3r2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-6.666666667 + 1.666666667r + r2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 1.666666667r + 6.666666667 + r2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 1.666666667r + r2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 1.666666667r + r2 = 0 + 6.666666667
1.666666667r + r2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
1.666666667r + r2 = 6.666666667

The r term is 1.666666667r.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667r + 0.6944444447 + r2 = 6.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667r + r2 = 6.666666667 + 0.6944444447

Combine like terms: 6.666666667 + 0.6944444447 = 7.3611111117
0.6944444447 + 1.666666667r + r2 = 7.3611111117

Factor a perfect square on the left side:
(r + 0.8333333335)(r + 0.8333333335) = 7.3611111117

Calculate the square root of the right side: 2.713136766

Break this problem into two subproblems by setting 
(r + 0.8333333335) equal to 2.713136766 and -2.713136766.

Subproblem 1

r + 0.8333333335 = 2.713136766 Simplifying r + 0.8333333335 = 2.713136766 Reorder the terms: 0.8333333335 + r = 2.713136766 Solving 0.8333333335 + r = 2.713136766 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + r = 2.713136766 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + r = 2.713136766 + -0.8333333335 r = 2.713136766 + -0.8333333335 Combine like terms: 2.713136766 + -0.8333333335 = 1.8798034325 r = 1.8798034325 Simplifying r = 1.8798034325

Subproblem 2

r + 0.8333333335 = -2.713136766 Simplifying r + 0.8333333335 = -2.713136766 Reorder the terms: 0.8333333335 + r = -2.713136766 Solving 0.8333333335 + r = -2.713136766 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + r = -2.713136766 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + r = -2.713136766 + -0.8333333335 r = -2.713136766 + -0.8333333335 Combine like terms: -2.713136766 + -0.8333333335 = -3.5464700995 r = -3.5464700995 Simplifying r = -3.5464700995

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.8798034325, -3.5464700995}

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