2r^2-5r-6=0

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Solution for 2r^2-5r-6=0 equation:


Simplifying
2r2 + -5r + -6 = 0

Reorder the terms:
-6 + -5r + 2r2 = 0

Solving
-6 + -5r + 2r2 = 0

Solving for variable 'r'.

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

Divide each side by '2'.
-3 + -2.5r + r2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2.5r + 3 + r2 = 0 + 3

Reorder the terms:
-3 + 3 + -2.5r + r2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2.5r + r2 = 0 + 3
-2.5r + r2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2.5r + r2 = 3

The r term is -2.5r.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5r + 1.5625 + r2 = 3 + 1.5625

Reorder the terms:
1.5625 + -2.5r + r2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + -2.5r + r2 = 4.5625

Factor a perfect square on the left side:
(r + -1.25)(r + -1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(r + -1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1

r + -1.25 = 2.136000936 Simplifying r + -1.25 = 2.136000936 Reorder the terms: -1.25 + r = 2.136000936 Solving -1.25 + r = 2.136000936 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + r = 2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + r = 2.136000936 + 1.25 r = 2.136000936 + 1.25 Combine like terms: 2.136000936 + 1.25 = 3.386000936 r = 3.386000936 Simplifying r = 3.386000936

Subproblem 2

r + -1.25 = -2.136000936 Simplifying r + -1.25 = -2.136000936 Reorder the terms: -1.25 + r = -2.136000936 Solving -1.25 + r = -2.136000936 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + r = -2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + r = -2.136000936 + 1.25 r = -2.136000936 + 1.25 Combine like terms: -2.136000936 + 1.25 = -0.886000936 r = -0.886000936 Simplifying r = -0.886000936

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.386000936, -0.886000936}

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