r^2-4r-7=0

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Solution for r^2-4r-7=0 equation: 


Simplifying
r2 + -4r + -7 = 0

Reorder the terms:
-7 + -4r + r2 = 0

Solving
-7 + -4r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -4r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + -4r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4r + r2 = 0 + 7
-4r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
-4r + r2 = 7

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 = 7 + 4

Reorder the terms:
4 + -4r + r2 = 7 + 4

Combine like terms: 7 + 4 = 11
4 + -4r + r2 = 11

Factor a perfect square on the left side:
(r + -2)(r + -2) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(r + -2) equal to 3.31662479 and -3.31662479.


Subproblem 1
r + -2 = 3.31662479

Simplifying
r + -2 = 3.31662479

Reorder the terms:
-2 + r = 3.31662479

Solving
-2 + r = 3.31662479

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 = 3.31662479 + 2

Combine like terms: -2 + 2 = 0
0 + r = 3.31662479 + 2
r = 3.31662479 + 2

Combine like terms: 3.31662479 + 2 = 5.31662479
r = 5.31662479

Simplifying
r = 5.31662479


Subproblem 2
r + -2 = -3.31662479

Simplifying
r + -2 = -3.31662479

Reorder the terms:
-2 + r = -3.31662479

Solving
-2 + r = -3.31662479

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 = -3.31662479 + 2

Combine like terms: -2 + 2 = 0
0 + r = -3.31662479 + 2
r = -3.31662479 + 2

Combine like terms: -3.31662479 + 2 = -1.31662479
r = -1.31662479

Simplifying
r = -1.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.31662479, -1.31662479}

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