r^2-7r=2

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


Simplifying
r2 + -7r = 2

Reorder the terms:
-7r + r2 = 2

Solving
-7r + r2 = 2

Solving for variable 'r'.

Reorder the terms:
-2 + -7r + r2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -7r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -7r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -7r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7r + r2 = 0 + 2
-7r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-7r + r2 = 2

The r term is -7r.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7r + 12.25 + r2 = 2 + 12.25

Reorder the terms:
12.25 + -7r + r2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + -7r + r2 = 14.25

Factor a perfect square on the left side:
(r + -3.5)(r + -3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(r + -3.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

r + -3.5 = 3.774917218 Simplifying r + -3.5 = 3.774917218 Reorder the terms: -3.5 + r = 3.774917218 Solving -3.5 + r = 3.774917218 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = 3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 3.774917218 + 3.5 r = 3.774917218 + 3.5 Combine like terms: 3.774917218 + 3.5 = 7.274917218 r = 7.274917218 Simplifying r = 7.274917218

Subproblem 2

r + -3.5 = -3.774917218 Simplifying r + -3.5 = -3.774917218 Reorder the terms: -3.5 + r = -3.774917218 Solving -3.5 + r = -3.774917218 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = -3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -3.774917218 + 3.5 r = -3.774917218 + 3.5 Combine like terms: -3.774917218 + 3.5 = -0.274917218 r = -0.274917218 Simplifying r = -0.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.274917218, -0.274917218}

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