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Simplifying r2 + 10r + -72 = 0 Reorder the terms: -72 + 10r + r2 = 0 Solving -72 + 10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 10r + 72 + r2 = 0 + 72 Reorder the terms: -72 + 72 + 10r + r2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 10r + r2 = 0 + 72 10r + r2 = 0 + 72 Combine like terms: 0 + 72 = 72 10r + r2 = 72 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = 72 + 25 Reorder the terms: 25 + 10r + r2 = 72 + 25 Combine like terms: 72 + 25 = 97 25 + 10r + r2 = 97 Factor a perfect square on the left side: (r + 5)(r + 5) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (r + 5) equal to 9.848857802 and -9.848857802.Subproblem 1
r + 5 = 9.848857802 Simplifying r + 5 = 9.848857802 Reorder the terms: 5 + r = 9.848857802 Solving 5 + r = 9.848857802 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 9.848857802 + -5 Combine like terms: 5 + -5 = 0 0 + r = 9.848857802 + -5 r = 9.848857802 + -5 Combine like terms: 9.848857802 + -5 = 4.848857802 r = 4.848857802 Simplifying r = 4.848857802Subproblem 2
r + 5 = -9.848857802 Simplifying r + 5 = -9.848857802 Reorder the terms: 5 + r = -9.848857802 Solving 5 + r = -9.848857802 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -9.848857802 + -5 Combine like terms: 5 + -5 = 0 0 + r = -9.848857802 + -5 r = -9.848857802 + -5 Combine like terms: -9.848857802 + -5 = -14.848857802 r = -14.848857802 Simplifying r = -14.848857802Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.848857802, -14.848857802}
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