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Simplifying 8r2 + -48r + -32 = 0 Reorder the terms: -32 + -48r + 8r2 = 0 Solving -32 + -48r + 8r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '8'. 8(-4 + -6r + r2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-4 + -6r + r2)' equal to zero and attempt to solve: Simplifying -4 + -6r + r2 = 0 Solving -4 + -6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -6r + 4 + r2 = 0 + 4 Reorder the terms: -4 + 4 + -6r + r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6r + r2 = 0 + 4 -6r + r2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6r + r2 = 4 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 = 4 + 9 Reorder the terms: 9 + -6r + r2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + -6r + r2 = 13 Factor a perfect square on the left side: (r + -3)(r + -3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (r + -3) equal to 3.605551275 and -3.605551275.Subproblem 1
r + -3 = 3.605551275 Simplifying r + -3 = 3.605551275 Reorder the terms: -3 + r = 3.605551275 Solving -3 + r = 3.605551275 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 = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + r = 3.605551275 + 3 r = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 r = 6.605551275 Simplifying r = 6.605551275Subproblem 2
r + -3 = -3.605551275 Simplifying r + -3 = -3.605551275 Reorder the terms: -3 + r = -3.605551275 Solving -3 + r = -3.605551275 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 = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + r = -3.605551275 + 3 r = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 r = -0.605551275 Simplifying r = -0.605551275Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.605551275, -0.605551275}Solution
r = {6.605551275, -0.605551275}
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