r^2-r=47

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Solution for r^2-r=47 equation:


Simplifying
r2 + -1r = 47

Reorder the terms:
-1r + r2 = 47

Solving
-1r + r2 = 47

Solving for variable 'r'.

Reorder the terms:
-47 + -1r + r2 = 47 + -47

Combine like terms: 47 + -47 = 0
-47 + -1r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -1r + 47 + r2 = 0 + 47

Reorder the terms:
-47 + 47 + -1r + r2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -1r + r2 = 0 + 47
-1r + r2 = 0 + 47

Combine like terms: 0 + 47 = 47
-1r + r2 = 47

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 = 47 + 0.25

Reorder the terms:
0.25 + -1r + r2 = 47 + 0.25

Combine like terms: 47 + 0.25 = 47.25
0.25 + -1r + r2 = 47.25

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(r + -0.5) equal to 6.873863542 and -6.873863542.

Subproblem 1

r + -0.5 = 6.873863542 Simplifying r + -0.5 = 6.873863542 Reorder the terms: -0.5 + r = 6.873863542 Solving -0.5 + r = 6.873863542 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 = 6.873863542 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 6.873863542 + 0.5 r = 6.873863542 + 0.5 Combine like terms: 6.873863542 + 0.5 = 7.373863542 r = 7.373863542 Simplifying r = 7.373863542

Subproblem 2

r + -0.5 = -6.873863542 Simplifying r + -0.5 = -6.873863542 Reorder the terms: -0.5 + r = -6.873863542 Solving -0.5 + r = -6.873863542 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 = -6.873863542 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -6.873863542 + 0.5 r = -6.873863542 + 0.5 Combine like terms: -6.873863542 + 0.5 = -6.373863542 r = -6.373863542 Simplifying r = -6.373863542

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.373863542, -6.373863542}

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