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Simplifying -4r2 + 80r + -360 = 0 Reorder the terms: -360 + 80r + -4r2 = 0 Solving -360 + 80r + -4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(-90 + 20r + -1r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-90 + 20r + -1r2)' equal to zero and attempt to solve: Simplifying -90 + 20r + -1r2 = 0 Solving -90 + 20r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 90 + -20r + r2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + -20r + -90 + r2 = 0 + -90 Reorder the terms: 90 + -90 + -20r + r2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -20r + r2 = 0 + -90 -20r + r2 = 0 + -90 Combine like terms: 0 + -90 = -90 -20r + r2 = -90 The r term is -20r. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20r + 100 + r2 = -90 + 100 Reorder the terms: 100 + -20r + r2 = -90 + 100 Combine like terms: -90 + 100 = 10 100 + -20r + r2 = 10 Factor a perfect square on the left side: (r + -10)(r + -10) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (r + -10) equal to 3.16227766 and -3.16227766.Subproblem 1
r + -10 = 3.16227766 Simplifying r + -10 = 3.16227766 Reorder the terms: -10 + r = 3.16227766 Solving -10 + r = 3.16227766 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 3.16227766 + 10 Combine like terms: -10 + 10 = 0 0 + r = 3.16227766 + 10 r = 3.16227766 + 10 Combine like terms: 3.16227766 + 10 = 13.16227766 r = 13.16227766 Simplifying r = 13.16227766Subproblem 2
r + -10 = -3.16227766 Simplifying r + -10 = -3.16227766 Reorder the terms: -10 + r = -3.16227766 Solving -10 + r = -3.16227766 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -3.16227766 + 10 Combine like terms: -10 + 10 = 0 0 + r = -3.16227766 + 10 r = -3.16227766 + 10 Combine like terms: -3.16227766 + 10 = 6.83772234 r = 6.83772234 Simplifying r = 6.83772234Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.16227766, 6.83772234}Solution
r = {13.16227766, 6.83772234}
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