4r^2-r-201=0

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Solution for 4r^2-r-201=0 equation:


Simplifying
4r2 + -1r + -201 = 0

Reorder the terms:
-201 + -1r + 4r2 = 0

Solving
-201 + -1r + 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'.
-50.25 + -0.25r + r2 = 0

Move the constant term to the right:

Add '50.25' to each side of the equation.
-50.25 + -0.25r + 50.25 + r2 = 0 + 50.25

Reorder the terms:
-50.25 + 50.25 + -0.25r + r2 = 0 + 50.25

Combine like terms: -50.25 + 50.25 = 0.00
0.00 + -0.25r + r2 = 0 + 50.25
-0.25r + r2 = 0 + 50.25

Combine like terms: 0 + 50.25 = 50.25
-0.25r + r2 = 50.25

The r term is -0.25r.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25r + 0.015625 + r2 = 50.25 + 0.015625

Reorder the terms:
0.015625 + -0.25r + r2 = 50.25 + 0.015625

Combine like terms: 50.25 + 0.015625 = 50.265625
0.015625 + -0.25r + r2 = 50.265625

Factor a perfect square on the left side:
(r + -0.125)(r + -0.125) = 50.265625

Calculate the square root of the right side: 7.089825456

Break this problem into two subproblems by setting 
(r + -0.125) equal to 7.089825456 and -7.089825456.

Subproblem 1

r + -0.125 = 7.089825456 Simplifying r + -0.125 = 7.089825456 Reorder the terms: -0.125 + r = 7.089825456 Solving -0.125 + r = 7.089825456 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + r = 7.089825456 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + r = 7.089825456 + 0.125 r = 7.089825456 + 0.125 Combine like terms: 7.089825456 + 0.125 = 7.214825456 r = 7.214825456 Simplifying r = 7.214825456

Subproblem 2

r + -0.125 = -7.089825456 Simplifying r + -0.125 = -7.089825456 Reorder the terms: -0.125 + r = -7.089825456 Solving -0.125 + r = -7.089825456 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + r = -7.089825456 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + r = -7.089825456 + 0.125 r = -7.089825456 + 0.125 Combine like terms: -7.089825456 + 0.125 = -6.964825456 r = -6.964825456 Simplifying r = -6.964825456

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.214825456, -6.964825456}

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