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Simplifying -2r2 + 32r + 42 = 0 Reorder the terms: 42 + 32r + -2r2 = 0 Solving 42 + 32r + -2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 16r + -1r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 16r + -1r2)' equal to zero and attempt to solve: Simplifying 21 + 16r + -1r2 = 0 Solving 21 + 16r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -16r + r2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -16r + 21 + r2 = 0 + 21 Reorder the terms: -21 + 21 + -16r + r2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -16r + r2 = 0 + 21 -16r + r2 = 0 + 21 Combine like terms: 0 + 21 = 21 -16r + r2 = 21 The r term is -16r. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16r + 64 + r2 = 21 + 64 Reorder the terms: 64 + -16r + r2 = 21 + 64 Combine like terms: 21 + 64 = 85 64 + -16r + r2 = 85 Factor a perfect square on the left side: (r + -8)(r + -8) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (r + -8) equal to 9.219544457 and -9.219544457.Subproblem 1
r + -8 = 9.219544457 Simplifying r + -8 = 9.219544457 Reorder the terms: -8 + r = 9.219544457 Solving -8 + r = 9.219544457 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = 9.219544457 + 8 Combine like terms: -8 + 8 = 0 0 + r = 9.219544457 + 8 r = 9.219544457 + 8 Combine like terms: 9.219544457 + 8 = 17.219544457 r = 17.219544457 Simplifying r = 17.219544457Subproblem 2
r + -8 = -9.219544457 Simplifying r + -8 = -9.219544457 Reorder the terms: -8 + r = -9.219544457 Solving -8 + r = -9.219544457 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = -9.219544457 + 8 Combine like terms: -8 + 8 = 0 0 + r = -9.219544457 + 8 r = -9.219544457 + 8 Combine like terms: -9.219544457 + 8 = -1.219544457 r = -1.219544457 Simplifying r = -1.219544457Solution
The solution to the problem is based on the solutions from the subproblems. r = {17.219544457, -1.219544457}Solution
r = {17.219544457, -1.219544457}
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