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Simplifying 3r2 + 18r = 24 Reorder the terms: 18r + 3r2 = 24 Solving 18r + 3r2 = 24 Solving for variable 'r'. Reorder the terms: -24 + 18r + 3r2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 18r + 3r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 6r + r2) = 0 Ignore the factor 3.Subproblem 1
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 = 1.123105626 r = 1.123105626 Simplifying r = 1.123105626Subproblem 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 = -7.123105626 r = -7.123105626 Simplifying r = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.123105626, -7.123105626}Solution
r = {1.123105626, -7.123105626}
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