r^2-2r-43=0

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Solution for r^2-2r-43=0 equation:


Simplifying
r2 + -2r + -43 = 0

Reorder the terms:
-43 + -2r + r2 = 0

Solving
-43 + -2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -2r + 43 + r2 = 0 + 43

Reorder the terms:
-43 + 43 + -2r + r2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -2r + r2 = 0 + 43
-2r + r2 = 0 + 43

Combine like terms: 0 + 43 = 43
-2r + r2 = 43

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 43 + 1

Reorder the terms:
1 + -2r + r2 = 43 + 1

Combine like terms: 43 + 1 = 44
1 + -2r + r2 = 44

Factor a perfect square on the left side:
(r + -1)(r + -1) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(r + -1) equal to 6.633249581 and -6.633249581.

Subproblem 1

r + -1 = 6.633249581 Simplifying r + -1 = 6.633249581 Reorder the terms: -1 + r = 6.633249581 Solving -1 + r = 6.633249581 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + r = 6.633249581 + 1 r = 6.633249581 + 1 Combine like terms: 6.633249581 + 1 = 7.633249581 r = 7.633249581 Simplifying r = 7.633249581

Subproblem 2

r + -1 = -6.633249581 Simplifying r + -1 = -6.633249581 Reorder the terms: -1 + r = -6.633249581 Solving -1 + r = -6.633249581 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + r = -6.633249581 + 1 r = -6.633249581 + 1 Combine like terms: -6.633249581 + 1 = -5.633249581 r = -5.633249581 Simplifying r = -5.633249581

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.633249581, -5.633249581}

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