r^2-4r-31=0

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Solution for r^2-4r-31=0 equation:


Simplifying
r2 + -4r + -31 = 0

Reorder the terms:
-31 + -4r + r2 = 0

Solving
-31 + -4r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -4r + 31 + r2 = 0 + 31

Reorder the terms:
-31 + 31 + -4r + r2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -4r + r2 = 0 + 31
-4r + r2 = 0 + 31

Combine like terms: 0 + 31 = 31
-4r + r2 = 31

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 31 + 4

Reorder the terms:
4 + -4r + r2 = 31 + 4

Combine like terms: 31 + 4 = 35
4 + -4r + r2 = 35

Factor a perfect square on the left side:
(r + -2)(r + -2) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(r + -2) equal to 5.916079783 and -5.916079783.

Subproblem 1

r + -2 = 5.916079783 Simplifying r + -2 = 5.916079783 Reorder the terms: -2 + r = 5.916079783 Solving -2 + r = 5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 5.916079783 + 2 Combine like terms: -2 + 2 = 0 0 + r = 5.916079783 + 2 r = 5.916079783 + 2 Combine like terms: 5.916079783 + 2 = 7.916079783 r = 7.916079783 Simplifying r = 7.916079783

Subproblem 2

r + -2 = -5.916079783 Simplifying r + -2 = -5.916079783 Reorder the terms: -2 + r = -5.916079783 Solving -2 + r = -5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -5.916079783 + 2 Combine like terms: -2 + 2 = 0 0 + r = -5.916079783 + 2 r = -5.916079783 + 2 Combine like terms: -5.916079783 + 2 = -3.916079783 r = -3.916079783 Simplifying r = -3.916079783

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.916079783, -3.916079783}

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