8r^2+5r-11=0

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Solution for 8r^2+5r-11=0 equation:


Simplifying
8r2 + 5r + -11 = 0

Reorder the terms:
-11 + 5r + 8r2 = 0

Solving
-11 + 5r + 8r2 = 0

Solving for variable 'r'.

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

Divide each side by '8'.
-1.375 + 0.625r + r2 = 0

Move the constant term to the right:

Add '1.375' to each side of the equation.
-1.375 + 0.625r + 1.375 + r2 = 0 + 1.375

Reorder the terms:
-1.375 + 1.375 + 0.625r + r2 = 0 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + 0.625r + r2 = 0 + 1.375
0.625r + r2 = 0 + 1.375

Combine like terms: 0 + 1.375 = 1.375
0.625r + r2 = 1.375

The r term is 0.625r.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625r + 0.09765625 + r2 = 1.375 + 0.09765625

Reorder the terms:
0.09765625 + 0.625r + r2 = 1.375 + 0.09765625

Combine like terms: 1.375 + 0.09765625 = 1.47265625
0.09765625 + 0.625r + r2 = 1.47265625

Factor a perfect square on the left side:
(r + 0.3125)(r + 0.3125) = 1.47265625

Calculate the square root of the right side: 1.21353049

Break this problem into two subproblems by setting 
(r + 0.3125) equal to 1.21353049 and -1.21353049.

Subproblem 1

r + 0.3125 = 1.21353049 Simplifying r + 0.3125 = 1.21353049 Reorder the terms: 0.3125 + r = 1.21353049 Solving 0.3125 + r = 1.21353049 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + r = 1.21353049 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + r = 1.21353049 + -0.3125 r = 1.21353049 + -0.3125 Combine like terms: 1.21353049 + -0.3125 = 0.90103049 r = 0.90103049 Simplifying r = 0.90103049

Subproblem 2

r + 0.3125 = -1.21353049 Simplifying r + 0.3125 = -1.21353049 Reorder the terms: 0.3125 + r = -1.21353049 Solving 0.3125 + r = -1.21353049 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + r = -1.21353049 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + r = -1.21353049 + -0.3125 r = -1.21353049 + -0.3125 Combine like terms: -1.21353049 + -0.3125 = -1.52603049 r = -1.52603049 Simplifying r = -1.52603049

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.90103049, -1.52603049}

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