2r^2=-2r+5

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Solution for 2r^2=-2r+5 equation:


Simplifying
2r2 = -2r + 5

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

Solving
2r2 = 5 + -2r

Solving for variable 'r'.

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

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

Combine like terms: 5 + -5 = 0
-5 + 2r + 2r2 = 0 + -2r + 2r
-5 + 2r + 2r2 = -2r + 2r

Combine like terms: -2r + 2r = 0
-5 + 2r + 2r2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + r + r2 = 0 + 2.5
r + r2 = 0 + 2.5

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

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.
 + 0.25 + r2 = 2.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
1.25 + r2 = 2.75

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(r + 0.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

r + 0.5 = 1.658312395 Simplifying r + 0.5 = 1.658312395 Reorder the terms: 0.5 + r = 1.658312395 Solving 0.5 + r = 1.658312395 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 = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 1.658312395 + -0.5 r = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 r = 1.158312395 Simplifying r = 1.158312395

Subproblem 2

r + 0.5 = -1.658312395 Simplifying r + 0.5 = -1.658312395 Reorder the terms: 0.5 + r = -1.658312395 Solving 0.5 + r = -1.658312395 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 = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -1.658312395 + -0.5 r = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 r = -2.158312395 Simplifying r = -2.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.158312395, -2.158312395}

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