r^2-7r=6

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Solution for r^2-7r=6 equation:


Simplifying
r2 + -7r = 6

Reorder the terms:
-7r + r2 = 6

Solving
-7r + r2 = 6

Solving for variable 'r'.

Reorder the terms:
-6 + -7r + r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -7r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -7r + 6 + r2 = 0 + 6

Reorder the terms:
-6 + 6 + -7r + r2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7r + r2 = 0 + 6
-7r + r2 = 0 + 6

Combine like terms: 0 + 6 = 6
-7r + r2 = 6

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 = 6 + 12.25

Reorder the terms:
12.25 + -7r + r2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + -7r + r2 = 18.25

Factor a perfect square on the left side:
(r + -3.5)(r + -3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(r + -3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

r + -3.5 = 4.272001873 Simplifying r + -3.5 = 4.272001873 Reorder the terms: -3.5 + r = 4.272001873 Solving -3.5 + r = 4.272001873 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 = 4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 4.272001873 + 3.5 r = 4.272001873 + 3.5 Combine like terms: 4.272001873 + 3.5 = 7.772001873 r = 7.772001873 Simplifying r = 7.772001873

Subproblem 2

r + -3.5 = -4.272001873 Simplifying r + -3.5 = -4.272001873 Reorder the terms: -3.5 + r = -4.272001873 Solving -3.5 + r = -4.272001873 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 = -4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -4.272001873 + 3.5 r = -4.272001873 + 3.5 Combine like terms: -4.272001873 + 3.5 = -0.772001873 r = -0.772001873 Simplifying r = -0.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.772001873, -0.772001873}

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