4r^2=17r+1

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Solution for 4r^2=17r+1 equation:


Simplifying
4r2 = 17r + 1

Reorder the terms:
4r2 = 1 + 17r

Solving
4r2 = 1 + 17r

Solving for variable 'r'.

Reorder the terms:
-1 + -17r + 4r2 = 1 + 17r + -1 + -17r

Reorder the terms:
-1 + -17r + 4r2 = 1 + -1 + 17r + -17r

Combine like terms: 1 + -1 = 0
-1 + -17r + 4r2 = 0 + 17r + -17r
-1 + -17r + 4r2 = 17r + -17r

Combine like terms: 17r + -17r = 0
-1 + -17r + 4r2 = 0

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

Divide each side by '4'.
-0.25 + -4.25r + r2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -4.25r + 0.25 + r2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -4.25r + r2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -4.25r + r2 = 0 + 0.25
-4.25r + r2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-4.25r + r2 = 0.25

The r term is -4.25r.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25r + 4.515625 + r2 = 0.25 + 4.515625

Reorder the terms:
4.515625 + -4.25r + r2 = 0.25 + 4.515625

Combine like terms: 0.25 + 4.515625 = 4.765625
4.515625 + -4.25r + r2 = 4.765625

Factor a perfect square on the left side:
(r + -2.125)(r + -2.125) = 4.765625

Calculate the square root of the right side: 2.18303115

Break this problem into two subproblems by setting 
(r + -2.125) equal to 2.18303115 and -2.18303115.

Subproblem 1

r + -2.125 = 2.18303115 Simplifying r + -2.125 = 2.18303115 Reorder the terms: -2.125 + r = 2.18303115 Solving -2.125 + r = 2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + r = 2.18303115 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + r = 2.18303115 + 2.125 r = 2.18303115 + 2.125 Combine like terms: 2.18303115 + 2.125 = 4.30803115 r = 4.30803115 Simplifying r = 4.30803115

Subproblem 2

r + -2.125 = -2.18303115 Simplifying r + -2.125 = -2.18303115 Reorder the terms: -2.125 + r = -2.18303115 Solving -2.125 + r = -2.18303115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + r = -2.18303115 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + r = -2.18303115 + 2.125 r = -2.18303115 + 2.125 Combine like terms: -2.18303115 + 2.125 = -0.05803115 r = -0.05803115 Simplifying r = -0.05803115

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.30803115, -0.05803115}

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