r^2+6r-80=-10

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Solution for r^2+6r-80=-10 equation:


Simplifying
r2 + 6r + -80 = -10

Reorder the terms:
-80 + 6r + r2 = -10

Solving
-80 + 6r + r2 = -10

Solving for variable 'r'.

Reorder the terms:
-80 + 10 + 6r + r2 = -10 + 10

Combine like terms: -80 + 10 = -70
-70 + 6r + r2 = -10 + 10

Combine like terms: -10 + 10 = 0
-70 + 6r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 6r + 70 + r2 = 0 + 70

Reorder the terms:
-70 + 70 + 6r + r2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 6r + r2 = 0 + 70
6r + r2 = 0 + 70

Combine like terms: 0 + 70 = 70
6r + r2 = 70

The r term is 6r.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6r + 9 + r2 = 70 + 9

Reorder the terms:
9 + 6r + r2 = 70 + 9

Combine like terms: 70 + 9 = 79
9 + 6r + r2 = 79

Factor a perfect square on the left side:
(r + 3)(r + 3) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(r + 3) equal to 8.888194417 and -8.888194417.

Subproblem 1

r + 3 = 8.888194417 Simplifying r + 3 = 8.888194417 Reorder the terms: 3 + r = 8.888194417 Solving 3 + r = 8.888194417 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 8.888194417 + -3 Combine like terms: 3 + -3 = 0 0 + r = 8.888194417 + -3 r = 8.888194417 + -3 Combine like terms: 8.888194417 + -3 = 5.888194417 r = 5.888194417 Simplifying r = 5.888194417

Subproblem 2

r + 3 = -8.888194417 Simplifying r + 3 = -8.888194417 Reorder the terms: 3 + r = -8.888194417 Solving 3 + r = -8.888194417 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -8.888194417 + -3 Combine like terms: 3 + -3 = 0 0 + r = -8.888194417 + -3 r = -8.888194417 + -3 Combine like terms: -8.888194417 + -3 = -11.888194417 r = -11.888194417 Simplifying r = -11.888194417

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.888194417, -11.888194417}

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