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Simplifying 36 = r2 + -12r + 36 + r2 + -12r + 36 Reorder the terms: 36 = 36 + 36 + -12r + -12r + r2 + r2 Combine like terms: 36 + 36 = 72 36 = 72 + -12r + -12r + r2 + r2 Combine like terms: -12r + -12r = -24r 36 = 72 + -24r + r2 + r2 Combine like terms: r2 + r2 = 2r2 36 = 72 + -24r + 2r2 Solving 36 = 72 + -24r + 2r2 Solving for variable 'r'. Combine like terms: 36 + -72 = -36 -36 + 24r + -2r2 = 72 + -24r + 2r2 + -72 + 24r + -2r2 Reorder the terms: -36 + 24r + -2r2 = 72 + -72 + -24r + 24r + 2r2 + -2r2 Combine like terms: 72 + -72 = 0 -36 + 24r + -2r2 = 0 + -24r + 24r + 2r2 + -2r2 -36 + 24r + -2r2 = -24r + 24r + 2r2 + -2r2 Combine like terms: -24r + 24r = 0 -36 + 24r + -2r2 = 0 + 2r2 + -2r2 -36 + 24r + -2r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -36 + 24r + -2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 12r + -1r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 12r + -1r2)' equal to zero and attempt to solve: Simplifying -18 + 12r + -1r2 = 0 Solving -18 + 12r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -12r + r2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -12r + -18 + r2 = 0 + -18 Reorder the terms: 18 + -18 + -12r + r2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -12r + r2 = 0 + -18 -12r + r2 = 0 + -18 Combine like terms: 0 + -18 = -18 -12r + r2 = -18 The r term is -12r. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12r + 36 + r2 = -18 + 36 Reorder the terms: 36 + -12r + r2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + -12r + r2 = 18 Factor a perfect square on the left side: (r + -6)(r + -6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (r + -6) equal to 4.242640687 and -4.242640687.Subproblem 1
r + -6 = 4.242640687 Simplifying r + -6 = 4.242640687 Reorder the terms: -6 + r = 4.242640687 Solving -6 + r = 4.242640687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = 4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + r = 4.242640687 + 6 r = 4.242640687 + 6 Combine like terms: 4.242640687 + 6 = 10.242640687 r = 10.242640687 Simplifying r = 10.242640687Subproblem 2
r + -6 = -4.242640687 Simplifying r + -6 = -4.242640687 Reorder the terms: -6 + r = -4.242640687 Solving -6 + r = -4.242640687 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = -4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + r = -4.242640687 + 6 r = -4.242640687 + 6 Combine like terms: -4.242640687 + 6 = 1.757359313 r = 1.757359313 Simplifying r = 1.757359313Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.242640687, 1.757359313}Solution
r = {10.242640687, 1.757359313}
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