0=r^2+14.2r-760.5

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Solution for 0=r^2+14.2r-760.5 equation:


Simplifying
0 = r2 + 14.2r + -760.5

Reorder the terms:
0 = -760.5 + 14.2r + r2

Solving
0 = -760.5 + 14.2r + r2

Solving for variable 'r'.

Combine like terms: 0 + 760.5 = 760.5
760.5 + -14.2r + -1r2 = -760.5 + 14.2r + r2 + 760.5 + -14.2r + -1r2

Reorder the terms:
760.5 + -14.2r + -1r2 = -760.5 + 760.5 + 14.2r + -14.2r + r2 + -1r2

Combine like terms: -760.5 + 760.5 = 0.0
760.5 + -14.2r + -1r2 = 0.0 + 14.2r + -14.2r + r2 + -1r2
760.5 + -14.2r + -1r2 = 14.2r + -14.2r + r2 + -1r2

Combine like terms: 14.2r + -14.2r = 0.0
760.5 + -14.2r + -1r2 = 0.0 + r2 + -1r2
760.5 + -14.2r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
760.5 + -14.2r + -1r2 = 0

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

Divide each side by '-1'.
-760.5 + 14.2r + r2 = 0

Move the constant term to the right:

Add '760.5' to each side of the equation.
-760.5 + 14.2r + 760.5 + r2 = 0 + 760.5

Reorder the terms:
-760.5 + 760.5 + 14.2r + r2 = 0 + 760.5

Combine like terms: -760.5 + 760.5 = 0.0
0.0 + 14.2r + r2 = 0 + 760.5
14.2r + r2 = 0 + 760.5

Combine like terms: 0 + 760.5 = 760.5
14.2r + r2 = 760.5

The r term is 14.2r.  Take half its coefficient (7.1).
Square it (50.41) and add it to both sides.

Add '50.41' to each side of the equation.
14.2r + 50.41 + r2 = 760.5 + 50.41

Reorder the terms:
50.41 + 14.2r + r2 = 760.5 + 50.41

Combine like terms: 760.5 + 50.41 = 810.91
50.41 + 14.2r + r2 = 810.91

Factor a perfect square on the left side:
(r + 7.1)(r + 7.1) = 810.91

Calculate the square root of the right side: 28.476481524

Break this problem into two subproblems by setting 
(r + 7.1) equal to 28.476481524 and -28.476481524.

Subproblem 1

r + 7.1 = 28.476481524 Simplifying r + 7.1 = 28.476481524 Reorder the terms: 7.1 + r = 28.476481524 Solving 7.1 + r = 28.476481524 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.1' to each side of the equation. 7.1 + -7.1 + r = 28.476481524 + -7.1 Combine like terms: 7.1 + -7.1 = 0.0 0.0 + r = 28.476481524 + -7.1 r = 28.476481524 + -7.1 Combine like terms: 28.476481524 + -7.1 = 21.376481524 r = 21.376481524 Simplifying r = 21.376481524

Subproblem 2

r + 7.1 = -28.476481524 Simplifying r + 7.1 = -28.476481524 Reorder the terms: 7.1 + r = -28.476481524 Solving 7.1 + r = -28.476481524 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.1' to each side of the equation. 7.1 + -7.1 + r = -28.476481524 + -7.1 Combine like terms: 7.1 + -7.1 = 0.0 0.0 + r = -28.476481524 + -7.1 r = -28.476481524 + -7.1 Combine like terms: -28.476481524 + -7.1 = -35.576481524 r = -35.576481524 Simplifying r = -35.576481524

Solution

The solution to the problem is based on the solutions from the subproblems. r = {21.376481524, -35.576481524}

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