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Simplifying 8r2 + -16r + -40 = 0 Reorder the terms: -40 + -16r + 8r2 = 0 Solving -40 + -16r + 8r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + -2r + r2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -2r + r2)' equal to zero and attempt to solve: Simplifying -5 + -2r + r2 = 0 Solving -5 + -2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2r + 5 + r2 = 0 + 5 Reorder the terms: -5 + 5 + -2r + r2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2r + r2 = 0 + 5 -2r + r2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2r + r2 = 5 The r term is -2r. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r + 1 + r2 = 5 + 1 Reorder the terms: 1 + -2r + r2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2r + r2 = 6 Factor a perfect square on the left side: (r + -1)(r + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (r + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
r + -1 = 2.449489743 Simplifying r + -1 = 2.449489743 Reorder the terms: -1 + r = 2.449489743 Solving -1 + r = 2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + r = 2.449489743 + 1 r = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 r = 3.449489743 Simplifying r = 3.449489743Subproblem 2
r + -1 = -2.449489743 Simplifying r + -1 = -2.449489743 Reorder the terms: -1 + r = -2.449489743 Solving -1 + r = -2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + r = -2.449489743 + 1 r = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 r = -1.449489743 Simplifying r = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.449489743, -1.449489743}Solution
r = {3.449489743, -1.449489743}
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