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Simplifying r2 + 10r + -28 = 0 Reorder the terms: -28 + 10r + r2 = 0 Solving -28 + 10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 10r + 28 + r2 = 0 + 28 Reorder the terms: -28 + 28 + 10r + r2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 10r + r2 = 0 + 28 10r + r2 = 0 + 28 Combine like terms: 0 + 28 = 28 10r + r2 = 28 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 = 28 + 25 Reorder the terms: 25 + 10r + r2 = 28 + 25 Combine like terms: 28 + 25 = 53 25 + 10r + r2 = 53 Factor a perfect square on the left side: (r + 5)(r + 5) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (r + 5) equal to 7.280109889 and -7.280109889.Subproblem 1
r + 5 = 7.280109889 Simplifying r + 5 = 7.280109889 Reorder the terms: 5 + r = 7.280109889 Solving 5 + r = 7.280109889 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 = 7.280109889 + -5 Combine like terms: 5 + -5 = 0 0 + r = 7.280109889 + -5 r = 7.280109889 + -5 Combine like terms: 7.280109889 + -5 = 2.280109889 r = 2.280109889 Simplifying r = 2.280109889Subproblem 2
r + 5 = -7.280109889 Simplifying r + 5 = -7.280109889 Reorder the terms: 5 + r = -7.280109889 Solving 5 + r = -7.280109889 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 = -7.280109889 + -5 Combine like terms: 5 + -5 = 0 0 + r = -7.280109889 + -5 r = -7.280109889 + -5 Combine like terms: -7.280109889 + -5 = -12.280109889 r = -12.280109889 Simplifying r = -12.280109889Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.280109889, -12.280109889}
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