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Simplifying 20r2 + -28r + -80 = 0 Reorder the terms: -80 + -28r + 20r2 = 0 Solving -80 + -28r + 20r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + -7r + 5r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + -7r + 5r2)' equal to zero and attempt to solve: Simplifying -20 + -7r + 5r2 = 0 Solving -20 + -7r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -1.4r + r2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.4r + 4 + r2 = 0 + 4 Reorder the terms: -4 + 4 + -1.4r + r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.4r + r2 = 0 + 4 -1.4r + r2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.4r + r2 = 4 The r term is -1.4r. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4r + 0.49 + r2 = 4 + 0.49 Reorder the terms: 0.49 + -1.4r + r2 = 4 + 0.49 Combine like terms: 4 + 0.49 = 4.49 0.49 + -1.4r + r2 = 4.49 Factor a perfect square on the left side: (r + -0.7)(r + -0.7) = 4.49 Calculate the square root of the right side: 2.11896201 Break this problem into two subproblems by setting (r + -0.7) equal to 2.11896201 and -2.11896201.Subproblem 1
r + -0.7 = 2.11896201 Simplifying r + -0.7 = 2.11896201 Reorder the terms: -0.7 + r = 2.11896201 Solving -0.7 + r = 2.11896201 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + r = 2.11896201 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + r = 2.11896201 + 0.7 r = 2.11896201 + 0.7 Combine like terms: 2.11896201 + 0.7 = 2.81896201 r = 2.81896201 Simplifying r = 2.81896201Subproblem 2
r + -0.7 = -2.11896201 Simplifying r + -0.7 = -2.11896201 Reorder the terms: -0.7 + r = -2.11896201 Solving -0.7 + r = -2.11896201 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + r = -2.11896201 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + r = -2.11896201 + 0.7 r = -2.11896201 + 0.7 Combine like terms: -2.11896201 + 0.7 = -1.41896201 r = -1.41896201 Simplifying r = -1.41896201Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.81896201, -1.41896201}Solution
r = {2.81896201, -1.41896201}
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