4r^2-48r+86.4=0

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Solution for 4r^2-48r+86.4=0 equation:


Simplifying
4r2 + -48r + 86.4 = 0

Reorder the terms:
86.4 + -48r + 4r2 = 0

Solving
86.4 + -48r + 4r2 = 0

Solving for variable 'r'.

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

Divide each side by '4'.
21.6 + -12r + r2 = 0

Move the constant term to the right:

Add '-21.6' to each side of the equation.
21.6 + -12r + -21.6 + r2 = 0 + -21.6

Reorder the terms:
21.6 + -21.6 + -12r + r2 = 0 + -21.6

Combine like terms: 21.6 + -21.6 = 0.0
0.0 + -12r + r2 = 0 + -21.6
-12r + r2 = 0 + -21.6

Combine like terms: 0 + -21.6 = -21.6
-12r + r2 = -21.6

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 = -21.6 + 36

Reorder the terms:
36 + -12r + r2 = -21.6 + 36

Combine like terms: -21.6 + 36 = 14.4
36 + -12r + r2 = 14.4

Factor a perfect square on the left side:
(r + -6)(r + -6) = 14.4

Calculate the square root of the right side: 3.794733192

Break this problem into two subproblems by setting 
(r + -6) equal to 3.794733192 and -3.794733192.

Subproblem 1

r + -6 = 3.794733192 Simplifying r + -6 = 3.794733192 Reorder the terms: -6 + r = 3.794733192 Solving -6 + r = 3.794733192 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 = 3.794733192 + 6 Combine like terms: -6 + 6 = 0 0 + r = 3.794733192 + 6 r = 3.794733192 + 6 Combine like terms: 3.794733192 + 6 = 9.794733192 r = 9.794733192 Simplifying r = 9.794733192

Subproblem 2

r + -6 = -3.794733192 Simplifying r + -6 = -3.794733192 Reorder the terms: -6 + r = -3.794733192 Solving -6 + r = -3.794733192 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 = -3.794733192 + 6 Combine like terms: -6 + 6 = 0 0 + r = -3.794733192 + 6 r = -3.794733192 + 6 Combine like terms: -3.794733192 + 6 = 2.205266808 r = 2.205266808 Simplifying r = 2.205266808

Solution

The solution to the problem is based on the solutions from the subproblems. r = {9.794733192, 2.205266808}

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