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Simplifying 0 = 10r2 + -28r + -160 Reorder the terms: 0 = -160 + -28r + 10r2 Solving 0 = -160 + -28r + 10r2 Solving for variable 'r'. Combine like terms: 0 + 160 = 160 160 + 28r + -10r2 = -160 + -28r + 10r2 + 160 + 28r + -10r2 Reorder the terms: 160 + 28r + -10r2 = -160 + 160 + -28r + 28r + 10r2 + -10r2 Combine like terms: -160 + 160 = 0 160 + 28r + -10r2 = 0 + -28r + 28r + 10r2 + -10r2 160 + 28r + -10r2 = -28r + 28r + 10r2 + -10r2 Combine like terms: -28r + 28r = 0 160 + 28r + -10r2 = 0 + 10r2 + -10r2 160 + 28r + -10r2 = 10r2 + -10r2 Combine like terms: 10r2 + -10r2 = 0 160 + 28r + -10r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(80 + 14r + -5r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(80 + 14r + -5r2)' equal to zero and attempt to solve: Simplifying 80 + 14r + -5r2 = 0 Solving 80 + 14r + -5r2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -16 + -2.8r + r2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -2.8r + 16 + r2 = 0 + 16 Reorder the terms: -16 + 16 + -2.8r + r2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2.8r + r2 = 0 + 16 -2.8r + r2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2.8r + r2 = 16 The r term is -2.8r. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8r + 1.96 + r2 = 16 + 1.96 Reorder the terms: 1.96 + -2.8r + r2 = 16 + 1.96 Combine like terms: 16 + 1.96 = 17.96 1.96 + -2.8r + r2 = 17.96 Factor a perfect square on the left side: (r + -1.4)(r + -1.4) = 17.96 Calculate the square root of the right side: 4.23792402 Break this problem into two subproblems by setting (r + -1.4) equal to 4.23792402 and -4.23792402.Subproblem 1
r + -1.4 = 4.23792402 Simplifying r + -1.4 = 4.23792402 Reorder the terms: -1.4 + r = 4.23792402 Solving -1.4 + r = 4.23792402 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + r = 4.23792402 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + r = 4.23792402 + 1.4 r = 4.23792402 + 1.4 Combine like terms: 4.23792402 + 1.4 = 5.63792402 r = 5.63792402 Simplifying r = 5.63792402Subproblem 2
r + -1.4 = -4.23792402 Simplifying r + -1.4 = -4.23792402 Reorder the terms: -1.4 + r = -4.23792402 Solving -1.4 + r = -4.23792402 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + r = -4.23792402 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + r = -4.23792402 + 1.4 r = -4.23792402 + 1.4 Combine like terms: -4.23792402 + 1.4 = -2.83792402 r = -2.83792402 Simplifying r = -2.83792402Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.63792402, -2.83792402}Solution
r = {5.63792402, -2.83792402}
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