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Simplifying r2 + -9r = 14 Reorder the terms: -9r + r2 = 14 Solving -9r + r2 = 14 Solving for variable 'r'. Reorder the terms: -14 + -9r + r2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -9r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -9r + 14 + r2 = 0 + 14 Reorder the terms: -14 + 14 + -9r + r2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -9r + r2 = 0 + 14 -9r + r2 = 0 + 14 Combine like terms: 0 + 14 = 14 -9r + r2 = 14 The r term is -9r. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9r + 20.25 + r2 = 14 + 20.25 Reorder the terms: 20.25 + -9r + r2 = 14 + 20.25 Combine like terms: 14 + 20.25 = 34.25 20.25 + -9r + r2 = 34.25 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (r + -4.5) equal to 5.852349955 and -5.852349955.Subproblem 1
r + -4.5 = 5.852349955 Simplifying r + -4.5 = 5.852349955 Reorder the terms: -4.5 + r = 5.852349955 Solving -4.5 + r = 5.852349955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = 5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 5.852349955 + 4.5 r = 5.852349955 + 4.5 Combine like terms: 5.852349955 + 4.5 = 10.352349955 r = 10.352349955 Simplifying r = 10.352349955Subproblem 2
r + -4.5 = -5.852349955 Simplifying r + -4.5 = -5.852349955 Reorder the terms: -4.5 + r = -5.852349955 Solving -4.5 + r = -5.852349955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = -5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -5.852349955 + 4.5 r = -5.852349955 + 4.5 Combine like terms: -5.852349955 + 4.5 = -1.352349955 r = -1.352349955 Simplifying r = -1.352349955Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.352349955, -1.352349955}
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