2r^2-9=2r

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Solution for 2r^2-9=2r equation:


Simplifying
2r2 + -9 = 2r

Reorder the terms:
-9 + 2r2 = 2r

Solving
-9 + 2r2 = 2r

Solving for variable 'r'.

Reorder the terms:
-9 + -2r + 2r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
-9 + -2r + 2r2 = 0

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

Divide each side by '2'.
-4.5 + -1r + r2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -1r + 4.5 + r2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -1r + r2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -1r + r2 = 0 + 4.5
-1r + r2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-1r + r2 = 4.5

The r term is -1r.  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.
-1r + 0.25 + r2 = 4.5 + 0.25

Reorder the terms:
0.25 + -1r + r2 = 4.5 + 0.25

Combine like terms: 4.5 + 0.25 = 4.75
0.25 + -1r + r2 = 4.75

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(r + -0.5) equal to 2.179449472 and -2.179449472.

Subproblem 1

r + -0.5 = 2.179449472 Simplifying r + -0.5 = 2.179449472 Reorder the terms: -0.5 + r = 2.179449472 Solving -0.5 + r = 2.179449472 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 = 2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 2.179449472 + 0.5 r = 2.179449472 + 0.5 Combine like terms: 2.179449472 + 0.5 = 2.679449472 r = 2.679449472 Simplifying r = 2.679449472

Subproblem 2

r + -0.5 = -2.179449472 Simplifying r + -0.5 = -2.179449472 Reorder the terms: -0.5 + r = -2.179449472 Solving -0.5 + r = -2.179449472 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 = -2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -2.179449472 + 0.5 r = -2.179449472 + 0.5 Combine like terms: -2.179449472 + 0.5 = -1.679449472 r = -1.679449472 Simplifying r = -1.679449472

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.679449472, -1.679449472}

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