0=r^2+10r-301.6

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Solution for 0=r^2+10r-301.6 equation:


Simplifying
0 = r2 + 10r + -301.6

Reorder the terms:
0 = -301.6 + 10r + r2

Solving
0 = -301.6 + 10r + r2

Solving for variable 'r'.

Combine like terms: 0 + 301.6 = 301.6
301.6 + -10r + -1r2 = -301.6 + 10r + r2 + 301.6 + -10r + -1r2

Reorder the terms:
301.6 + -10r + -1r2 = -301.6 + 301.6 + 10r + -10r + r2 + -1r2

Combine like terms: -301.6 + 301.6 = 0.0
301.6 + -10r + -1r2 = 0.0 + 10r + -10r + r2 + -1r2
301.6 + -10r + -1r2 = 10r + -10r + r2 + -1r2

Combine like terms: 10r + -10r = 0
301.6 + -10r + -1r2 = 0 + r2 + -1r2
301.6 + -10r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
301.6 + -10r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-301.6 + 10r + r2 = 0

Move the constant term to the right:

Add '301.6' to each side of the equation.
-301.6 + 10r + 301.6 + r2 = 0 + 301.6

Reorder the terms:
-301.6 + 301.6 + 10r + r2 = 0 + 301.6

Combine like terms: -301.6 + 301.6 = 0.0
0.0 + 10r + r2 = 0 + 301.6
10r + r2 = 0 + 301.6

Combine like terms: 0 + 301.6 = 301.6
10r + r2 = 301.6

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 = 301.6 + 25

Reorder the terms:
25 + 10r + r2 = 301.6 + 25

Combine like terms: 301.6 + 25 = 326.6
25 + 10r + r2 = 326.6

Factor a perfect square on the left side:
(r + 5)(r + 5) = 326.6

Calculate the square root of the right side: 18.07207791

Break this problem into two subproblems by setting 
(r + 5) equal to 18.07207791 and -18.07207791.

Subproblem 1

r + 5 = 18.07207791 Simplifying r + 5 = 18.07207791 Reorder the terms: 5 + r = 18.07207791 Solving 5 + r = 18.07207791 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 = 18.07207791 + -5 Combine like terms: 5 + -5 = 0 0 + r = 18.07207791 + -5 r = 18.07207791 + -5 Combine like terms: 18.07207791 + -5 = 13.07207791 r = 13.07207791 Simplifying r = 13.07207791

Subproblem 2

r + 5 = -18.07207791 Simplifying r + 5 = -18.07207791 Reorder the terms: 5 + r = -18.07207791 Solving 5 + r = -18.07207791 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 = -18.07207791 + -5 Combine like terms: 5 + -5 = 0 0 + r = -18.07207791 + -5 r = -18.07207791 + -5 Combine like terms: -18.07207791 + -5 = -23.07207791 r = -23.07207791 Simplifying r = -23.07207791

Solution

The solution to the problem is based on the solutions from the subproblems. r = {13.07207791, -23.07207791}

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