r^2-12r-38=10

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Solution for r^2-12r-38=10 equation:


Simplifying
r2 + -12r + -38 = 10

Reorder the terms:
-38 + -12r + r2 = 10

Solving
-38 + -12r + r2 = 10

Solving for variable 'r'.

Reorder the terms:
-38 + -10 + -12r + r2 = 10 + -10

Combine like terms: -38 + -10 = -48
-48 + -12r + r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-48 + -12r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -12r + 48 + r2 = 0 + 48

Reorder the terms:
-48 + 48 + -12r + r2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -12r + r2 = 0 + 48
-12r + r2 = 0 + 48

Combine like terms: 0 + 48 = 48
-12r + r2 = 48

The r term is -12r.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12r + 36 + r2 = 48 + 36

Reorder the terms:
36 + -12r + r2 = 48 + 36

Combine like terms: 48 + 36 = 84
36 + -12r + r2 = 84

Factor a perfect square on the left side:
(r + -6)(r + -6) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(r + -6) equal to 9.16515139 and -9.16515139.

Subproblem 1

r + -6 = 9.16515139 Simplifying r + -6 = 9.16515139 Reorder the terms: -6 + r = 9.16515139 Solving -6 + r = 9.16515139 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = 9.16515139 + 6 Combine like terms: -6 + 6 = 0 0 + r = 9.16515139 + 6 r = 9.16515139 + 6 Combine like terms: 9.16515139 + 6 = 15.16515139 r = 15.16515139 Simplifying r = 15.16515139

Subproblem 2

r + -6 = -9.16515139 Simplifying r + -6 = -9.16515139 Reorder the terms: -6 + r = -9.16515139 Solving -6 + r = -9.16515139 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = -9.16515139 + 6 Combine like terms: -6 + 6 = 0 0 + r = -9.16515139 + 6 r = -9.16515139 + 6 Combine like terms: -9.16515139 + 6 = -3.16515139 r = -3.16515139 Simplifying r = -3.16515139

Solution

The solution to the problem is based on the solutions from the subproblems. r = {15.16515139, -3.16515139}

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