0=r^2+15.6r-135.31

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Solution for 0=r^2+15.6r-135.31 equation:


Simplifying
0 = r2 + 15.6r + -135.31

Reorder the terms:
0 = -135.31 + 15.6r + r2

Solving
0 = -135.31 + 15.6r + r2

Solving for variable 'r'.

Combine like terms: 0 + 135.31 = 135.31
135.31 + -15.6r + -1r2 = -135.31 + 15.6r + r2 + 135.31 + -15.6r + -1r2

Reorder the terms:
135.31 + -15.6r + -1r2 = -135.31 + 135.31 + 15.6r + -15.6r + r2 + -1r2

Combine like terms: -135.31 + 135.31 = 0.00
135.31 + -15.6r + -1r2 = 0.00 + 15.6r + -15.6r + r2 + -1r2
135.31 + -15.6r + -1r2 = 15.6r + -15.6r + r2 + -1r2

Combine like terms: 15.6r + -15.6r = 0.0
135.31 + -15.6r + -1r2 = 0.0 + r2 + -1r2
135.31 + -15.6r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
135.31 + -15.6r + -1r2 = 0

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

Divide each side by '-1'.
-135.31 + 15.6r + r2 = 0

Move the constant term to the right:

Add '135.31' to each side of the equation.
-135.31 + 15.6r + 135.31 + r2 = 0 + 135.31

Reorder the terms:
-135.31 + 135.31 + 15.6r + r2 = 0 + 135.31

Combine like terms: -135.31 + 135.31 = 0.00
0.00 + 15.6r + r2 = 0 + 135.31
15.6r + r2 = 0 + 135.31

Combine like terms: 0 + 135.31 = 135.31
15.6r + r2 = 135.31

The r term is 15.6r.  Take half its coefficient (7.8).
Square it (60.84) and add it to both sides.

Add '60.84' to each side of the equation.
15.6r + 60.84 + r2 = 135.31 + 60.84

Reorder the terms:
60.84 + 15.6r + r2 = 135.31 + 60.84

Combine like terms: 135.31 + 60.84 = 196.15
60.84 + 15.6r + r2 = 196.15

Factor a perfect square on the left side:
(r + 7.8)(r + 7.8) = 196.15

Calculate the square root of the right side: 14.005356118

Break this problem into two subproblems by setting 
(r + 7.8) equal to 14.005356118 and -14.005356118.

Subproblem 1

r + 7.8 = 14.005356118 Simplifying r + 7.8 = 14.005356118 Reorder the terms: 7.8 + r = 14.005356118 Solving 7.8 + r = 14.005356118 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + r = 14.005356118 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + r = 14.005356118 + -7.8 r = 14.005356118 + -7.8 Combine like terms: 14.005356118 + -7.8 = 6.205356118 r = 6.205356118 Simplifying r = 6.205356118

Subproblem 2

r + 7.8 = -14.005356118 Simplifying r + 7.8 = -14.005356118 Reorder the terms: 7.8 + r = -14.005356118 Solving 7.8 + r = -14.005356118 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + r = -14.005356118 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + r = -14.005356118 + -7.8 r = -14.005356118 + -7.8 Combine like terms: -14.005356118 + -7.8 = -21.805356118 r = -21.805356118 Simplifying r = -21.805356118

Solution

The solution to the problem is based on the solutions from the subproblems. r = {6.205356118, -21.805356118}

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