-r^2=3r-3

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Solution for -r^2=3r-3 equation:


Simplifying
-1r2 = 3r + -3

Reorder the terms:
-1r2 = -3 + 3r

Solving
-1r2 = -3 + 3r

Solving for variable 'r'.

Reorder the terms:
3 + -3r + -1r2 = -3 + 3r + 3 + -3r

Reorder the terms:
3 + -3r + -1r2 = -3 + 3 + 3r + -3r

Combine like terms: -3 + 3 = 0
3 + -3r + -1r2 = 0 + 3r + -3r
3 + -3r + -1r2 = 3r + -3r

Combine like terms: 3r + -3r = 0
3 + -3r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + 3r + r2 = 0

Move the constant term to the right:

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

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

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

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

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 3 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + 3r + r2 = 5.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(r + 1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

r + 1.5 = 2.291287847 Simplifying r + 1.5 = 2.291287847 Reorder the terms: 1.5 + r = 2.291287847 Solving 1.5 + r = 2.291287847 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 2.291287847 + -1.5 r = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 r = 0.791287847 Simplifying r = 0.791287847

Subproblem 2

r + 1.5 = -2.291287847 Simplifying r + 1.5 = -2.291287847 Reorder the terms: 1.5 + r = -2.291287847 Solving 1.5 + r = -2.291287847 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -2.291287847 + -1.5 r = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 r = -3.791287847 Simplifying r = -3.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.791287847, -3.791287847}

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