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Simplifying r2 + -30r + 20 = 0 Reorder the terms: 20 + -30r + r2 = 0 Solving 20 + -30r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -30r + -20 + r2 = 0 + -20 Reorder the terms: 20 + -20 + -30r + r2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -30r + r2 = 0 + -20 -30r + r2 = 0 + -20 Combine like terms: 0 + -20 = -20 -30r + r2 = -20 The r term is -30r. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30r + 225 + r2 = -20 + 225 Reorder the terms: 225 + -30r + r2 = -20 + 225 Combine like terms: -20 + 225 = 205 225 + -30r + r2 = 205 Factor a perfect square on the left side: (r + -15)(r + -15) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (r + -15) equal to 14.317821063 and -14.317821063.Subproblem 1
r + -15 = 14.317821063 Simplifying r + -15 = 14.317821063 Reorder the terms: -15 + r = 14.317821063 Solving -15 + r = 14.317821063 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = 14.317821063 + 15 Combine like terms: -15 + 15 = 0 0 + r = 14.317821063 + 15 r = 14.317821063 + 15 Combine like terms: 14.317821063 + 15 = 29.317821063 r = 29.317821063 Simplifying r = 29.317821063Subproblem 2
r + -15 = -14.317821063 Simplifying r + -15 = -14.317821063 Reorder the terms: -15 + r = -14.317821063 Solving -15 + r = -14.317821063 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = -14.317821063 + 15 Combine like terms: -15 + 15 = 0 0 + r = -14.317821063 + 15 r = -14.317821063 + 15 Combine like terms: -14.317821063 + 15 = 0.682178937 r = 0.682178937 Simplifying r = 0.682178937Solution
The solution to the problem is based on the solutions from the subproblems. r = {29.317821063, 0.682178937}
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