r^2-10r=7

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Solution for r^2-10r=7 equation:


Simplifying
r2 + -10r = 7

Reorder the terms:
-10r + r2 = 7

Solving
-10r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + -10r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -10r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + -10r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10r + r2 = 0 + 7
-10r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
-10r + r2 = 7

The r term is -10r.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r + 25 + r2 = 7 + 25

Reorder the terms:
25 + -10r + r2 = 7 + 25

Combine like terms: 7 + 25 = 32
25 + -10r + r2 = 32

Factor a perfect square on the left side:
(r + -5)(r + -5) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(r + -5) equal to 5.656854249 and -5.656854249.

Subproblem 1

r + -5 = 5.656854249 Simplifying r + -5 = 5.656854249 Reorder the terms: -5 + r = 5.656854249 Solving -5 + r = 5.656854249 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + r = 5.656854249 + 5 r = 5.656854249 + 5 Combine like terms: 5.656854249 + 5 = 10.656854249 r = 10.656854249 Simplifying r = 10.656854249

Subproblem 2

r + -5 = -5.656854249 Simplifying r + -5 = -5.656854249 Reorder the terms: -5 + r = -5.656854249 Solving -5 + r = -5.656854249 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + r = -5.656854249 + 5 r = -5.656854249 + 5 Combine like terms: -5.656854249 + 5 = -0.656854249 r = -0.656854249 Simplifying r = -0.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. r = {10.656854249, -0.656854249}

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