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Simplifying 9r2 + 60r + -900 = 0 Reorder the terms: -900 + 60r + 9r2 = 0 Solving -900 + 60r + 9r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(-300 + 20r + 3r2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-300 + 20r + 3r2)' equal to zero and attempt to solve: Simplifying -300 + 20r + 3r2 = 0 Solving -300 + 20r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -100 + 6.666666667r + r2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 6.666666667r + 100 + r2 = 0 + 100 Reorder the terms: -100 + 100 + 6.666666667r + r2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 6.666666667r + r2 = 0 + 100 6.666666667r + r2 = 0 + 100 Combine like terms: 0 + 100 = 100 6.666666667r + r2 = 100 The r term is 6.666666667r. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667r + 11.11111112 + r2 = 100 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667r + r2 = 100 + 11.11111112 Combine like terms: 100 + 11.11111112 = 111.11111112 11.11111112 + 6.666666667r + r2 = 111.11111112 Factor a perfect square on the left side: (r + 3.333333334)(r + 3.333333334) = 111.11111112 Calculate the square root of the right side: 10.540925534 Break this problem into two subproblems by setting (r + 3.333333334) equal to 10.540925534 and -10.540925534.Subproblem 1
r + 3.333333334 = 10.540925534 Simplifying r + 3.333333334 = 10.540925534 Reorder the terms: 3.333333334 + r = 10.540925534 Solving 3.333333334 + r = 10.540925534 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + r = 10.540925534 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + r = 10.540925534 + -3.333333334 r = 10.540925534 + -3.333333334 Combine like terms: 10.540925534 + -3.333333334 = 7.2075922 r = 7.2075922 Simplifying r = 7.2075922Subproblem 2
r + 3.333333334 = -10.540925534 Simplifying r + 3.333333334 = -10.540925534 Reorder the terms: 3.333333334 + r = -10.540925534 Solving 3.333333334 + r = -10.540925534 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + r = -10.540925534 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + r = -10.540925534 + -3.333333334 r = -10.540925534 + -3.333333334 Combine like terms: -10.540925534 + -3.333333334 = -13.874258868 r = -13.874258868 Simplifying r = -13.874258868Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.2075922, -13.874258868}Solution
r = {7.2075922, -13.874258868}
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