4r^2-25r+20=0

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Solution for 4r^2-25r+20=0 equation:


Simplifying
4r2 + -25r + 20 = 0

Reorder the terms:
20 + -25r + 4r2 = 0

Solving
20 + -25r + 4r2 = 0

Solving for variable 'r'.

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

Divide each side by '4'.
5 + -6.25r + r2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -6.25r + -5 + r2 = 0 + -5

Reorder the terms:
5 + -5 + -6.25r + r2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6.25r + r2 = 0 + -5
-6.25r + r2 = 0 + -5

Combine like terms: 0 + -5 = -5
-6.25r + r2 = -5

The r term is -6.25r.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25r + 9.765625 + r2 = -5 + 9.765625

Reorder the terms:
9.765625 + -6.25r + r2 = -5 + 9.765625

Combine like terms: -5 + 9.765625 = 4.765625
9.765625 + -6.25r + r2 = 4.765625

Factor a perfect square on the left side:
(r + -3.125)(r + -3.125) = 4.765625

Calculate the square root of the right side: 2.18303115

Break this problem into two subproblems by setting 
(r + -3.125) equal to 2.18303115 and -2.18303115.

Subproblem 1

r + -3.125 = 2.18303115 Simplifying r + -3.125 = 2.18303115 Reorder the terms: -3.125 + r = 2.18303115 Solving -3.125 + r = 2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + r = 2.18303115 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + r = 2.18303115 + 3.125 r = 2.18303115 + 3.125 Combine like terms: 2.18303115 + 3.125 = 5.30803115 r = 5.30803115 Simplifying r = 5.30803115

Subproblem 2

r + -3.125 = -2.18303115 Simplifying r + -3.125 = -2.18303115 Reorder the terms: -3.125 + r = -2.18303115 Solving -3.125 + r = -2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + r = -2.18303115 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + r = -2.18303115 + 3.125 r = -2.18303115 + 3.125 Combine like terms: -2.18303115 + 3.125 = 0.94196885 r = 0.94196885 Simplifying r = 0.94196885

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.30803115, 0.94196885}

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