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Simplifying -2r2 + 49 + -21r = 0 Reorder the terms: 49 + -21r + -2r2 = 0 Solving 49 + -21r + -2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -24.5 + 10.5r + r2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + 10.5r + 24.5 + r2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + 10.5r + r2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + 10.5r + r2 = 0 + 24.5 10.5r + r2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 10.5r + r2 = 24.5 The r term is 10.5r. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5r + 27.5625 + r2 = 24.5 + 27.5625 Reorder the terms: 27.5625 + 10.5r + r2 = 24.5 + 27.5625 Combine like terms: 24.5 + 27.5625 = 52.0625 27.5625 + 10.5r + r2 = 52.0625 Factor a perfect square on the left side: (r + 5.25)(r + 5.25) = 52.0625 Calculate the square root of the right side: 7.215434845 Break this problem into two subproblems by setting (r + 5.25) equal to 7.215434845 and -7.215434845.Subproblem 1
r + 5.25 = 7.215434845 Simplifying r + 5.25 = 7.215434845 Reorder the terms: 5.25 + r = 7.215434845 Solving 5.25 + r = 7.215434845 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + r = 7.215434845 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + r = 7.215434845 + -5.25 r = 7.215434845 + -5.25 Combine like terms: 7.215434845 + -5.25 = 1.965434845 r = 1.965434845 Simplifying r = 1.965434845Subproblem 2
r + 5.25 = -7.215434845 Simplifying r + 5.25 = -7.215434845 Reorder the terms: 5.25 + r = -7.215434845 Solving 5.25 + r = -7.215434845 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + r = -7.215434845 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + r = -7.215434845 + -5.25 r = -7.215434845 + -5.25 Combine like terms: -7.215434845 + -5.25 = -12.465434845 r = -12.465434845 Simplifying r = -12.465434845Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.965434845, -12.465434845}
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