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Simplifying r5 + -6r4 + -8r3 = 0 Reorder the terms: -8r3 + -6r4 + r5 = 0 Solving -8r3 + -6r4 + r5 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r3'. r3(-8 + -6r + r2) = 0Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve: Simplifying r3 = 0 Solving r3 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-8 + -6r + r2)' equal to zero and attempt to solve: Simplifying -8 + -6r + r2 = 0 Solving -8 + -6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6r + 8 + r2 = 0 + 8 Reorder the terms: -8 + 8 + -6r + r2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6r + r2 = 0 + 8 -6r + r2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6r + r2 = 8 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 = 8 + 9 Reorder the terms: 9 + -6r + r2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6r + r2 = 17 Factor a perfect square on the left side: (r + -3)(r + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (r + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
r + -3 = 4.123105626 Simplifying r + -3 = 4.123105626 Reorder the terms: -3 + r = 4.123105626 Solving -3 + r = 4.123105626 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 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + r = 4.123105626 + 3 r = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 r = 7.123105626 Simplifying r = 7.123105626Subproblem 2
r + -3 = -4.123105626 Simplifying r + -3 = -4.123105626 Reorder the terms: -3 + r = -4.123105626 Solving -3 + r = -4.123105626 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 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + r = -4.123105626 + 3 r = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 r = -1.123105626 Simplifying r = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.123105626, -1.123105626}Solution
r = {7.123105626, -1.123105626}
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