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Simplifying r2 + -28r + 36 = 0 Reorder the terms: 36 + -28r + r2 = 0 Solving 36 + -28r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -28r + -36 + r2 = 0 + -36 Reorder the terms: 36 + -36 + -28r + r2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -28r + r2 = 0 + -36 -28r + r2 = 0 + -36 Combine like terms: 0 + -36 = -36 -28r + r2 = -36 The r term is -28r. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28r + 196 + r2 = -36 + 196 Reorder the terms: 196 + -28r + r2 = -36 + 196 Combine like terms: -36 + 196 = 160 196 + -28r + r2 = 160 Factor a perfect square on the left side: (r + -14)(r + -14) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (r + -14) equal to 12.649110641 and -12.649110641.Subproblem 1
r + -14 = 12.649110641 Simplifying r + -14 = 12.649110641 Reorder the terms: -14 + r = 12.649110641 Solving -14 + r = 12.649110641 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + r = 12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + r = 12.649110641 + 14 r = 12.649110641 + 14 Combine like terms: 12.649110641 + 14 = 26.649110641 r = 26.649110641 Simplifying r = 26.649110641Subproblem 2
r + -14 = -12.649110641 Simplifying r + -14 = -12.649110641 Reorder the terms: -14 + r = -12.649110641 Solving -14 + r = -12.649110641 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + r = -12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + r = -12.649110641 + 14 r = -12.649110641 + 14 Combine like terms: -12.649110641 + 14 = 1.350889359 r = 1.350889359 Simplifying r = 1.350889359Solution
The solution to the problem is based on the solutions from the subproblems. r = {26.649110641, 1.350889359}
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