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Simplifying -2r2 + 16r = -22 Reorder the terms: 16r + -2r2 = -22 Solving 16r + -2r2 = -22 Solving for variable 'r'. Reorder the terms: 22 + 16r + -2r2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + 16r + -2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 8r + -1r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 8r + -1r2)' equal to zero and attempt to solve: Simplifying 11 + 8r + -1r2 = 0 Solving 11 + 8r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -8r + r2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -8r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + -8r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -8r + r2 = 0 + 11 -8r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 -8r + r2 = 11 The r term is -8r. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8r + 16 + r2 = 11 + 16 Reorder the terms: 16 + -8r + r2 = 11 + 16 Combine like terms: 11 + 16 = 27 16 + -8r + r2 = 27 Factor a perfect square on the left side: (r + -4)(r + -4) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (r + -4) equal to 5.196152423 and -5.196152423.Subproblem 1
r + -4 = 5.196152423 Simplifying r + -4 = 5.196152423 Reorder the terms: -4 + r = 5.196152423 Solving -4 + r = 5.196152423 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + r = 5.196152423 + 4 r = 5.196152423 + 4 Combine like terms: 5.196152423 + 4 = 9.196152423 r = 9.196152423 Simplifying r = 9.196152423Subproblem 2
r + -4 = -5.196152423 Simplifying r + -4 = -5.196152423 Reorder the terms: -4 + r = -5.196152423 Solving -4 + r = -5.196152423 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = -5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + r = -5.196152423 + 4 r = -5.196152423 + 4 Combine like terms: -5.196152423 + 4 = -1.196152423 r = -1.196152423 Simplifying r = -1.196152423Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.196152423, -1.196152423}Solution
r = {9.196152423, -1.196152423}
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