2r^2+r-14=0

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Solution for 2r^2+r-14=0 equation:


Simplifying
2r2 + r + -14 = 0

Reorder the terms:
-14 + r + 2r2 = 0

Solving
-14 + r + 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'.
-7 + 0.5r + r2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 0.5r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + 0.5r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 0.5r + r2 = 0 + 7
0.5r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
0.5r + r2 = 7

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5r + 0.25 + r2 = 7 + 0.25

Reorder the terms:
0.25 + 0.5r + r2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + 0.5r + r2 = 7.25

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(r + 0.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

r + 0.5 = 2.692582404 Simplifying r + 0.5 = 2.692582404 Reorder the terms: 0.5 + r = 2.692582404 Solving 0.5 + r = 2.692582404 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 2.692582404 + -0.5 r = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 r = 2.192582404 Simplifying r = 2.192582404

Subproblem 2

r + 0.5 = -2.692582404 Simplifying r + 0.5 = -2.692582404 Reorder the terms: 0.5 + r = -2.692582404 Solving 0.5 + r = -2.692582404 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -2.692582404 + -0.5 r = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 r = -3.192582404 Simplifying r = -3.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.192582404, -3.192582404}

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