r^2-4r-91=7

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Solution for r^2-4r-91=7 equation:


Simplifying
r2 + -4r + -91 = 7

Reorder the terms:
-91 + -4r + r2 = 7

Solving
-91 + -4r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-91 + -7 + -4r + r2 = 7 + -7

Combine like terms: -91 + -7 = -98
-98 + -4r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-98 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + -4r + 98 + r2 = 0 + 98

Reorder the terms:
-98 + 98 + -4r + r2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + -4r + r2 = 0 + 98
-4r + r2 = 0 + 98

Combine like terms: 0 + 98 = 98
-4r + r2 = 98

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 = 98 + 4

Reorder the terms:
4 + -4r + r2 = 98 + 4

Combine like terms: 98 + 4 = 102
4 + -4r + r2 = 102

Factor a perfect square on the left side:
(r + -2)(r + -2) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(r + -2) equal to 10.099504938 and -10.099504938.

Subproblem 1

r + -2 = 10.099504938 Simplifying r + -2 = 10.099504938 Reorder the terms: -2 + r = 10.099504938 Solving -2 + r = 10.099504938 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 = 10.099504938 + 2 Combine like terms: -2 + 2 = 0 0 + r = 10.099504938 + 2 r = 10.099504938 + 2 Combine like terms: 10.099504938 + 2 = 12.099504938 r = 12.099504938 Simplifying r = 12.099504938

Subproblem 2

r + -2 = -10.099504938 Simplifying r + -2 = -10.099504938 Reorder the terms: -2 + r = -10.099504938 Solving -2 + r = -10.099504938 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 = -10.099504938 + 2 Combine like terms: -2 + 2 = 0 0 + r = -10.099504938 + 2 r = -10.099504938 + 2 Combine like terms: -10.099504938 + 2 = -8.099504938 r = -8.099504938 Simplifying r = -8.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. r = {12.099504938, -8.099504938}

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