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Simplifying r2 + 20r + -78 = 0 Reorder the terms: -78 + 20r + r2 = 0 Solving -78 + 20r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 20r + 78 + r2 = 0 + 78 Reorder the terms: -78 + 78 + 20r + r2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 20r + r2 = 0 + 78 20r + r2 = 0 + 78 Combine like terms: 0 + 78 = 78 20r + r2 = 78 The r term is 20r. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20r + 100 + r2 = 78 + 100 Reorder the terms: 100 + 20r + r2 = 78 + 100 Combine like terms: 78 + 100 = 178 100 + 20r + r2 = 178 Factor a perfect square on the left side: (r + 10)(r + 10) = 178 Calculate the square root of the right side: 13.341664064 Break this problem into two subproblems by setting (r + 10) equal to 13.341664064 and -13.341664064.Subproblem 1
r + 10 = 13.341664064 Simplifying r + 10 = 13.341664064 Reorder the terms: 10 + r = 13.341664064 Solving 10 + r = 13.341664064 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + r = 13.341664064 + -10 Combine like terms: 10 + -10 = 0 0 + r = 13.341664064 + -10 r = 13.341664064 + -10 Combine like terms: 13.341664064 + -10 = 3.341664064 r = 3.341664064 Simplifying r = 3.341664064Subproblem 2
r + 10 = -13.341664064 Simplifying r + 10 = -13.341664064 Reorder the terms: 10 + r = -13.341664064 Solving 10 + r = -13.341664064 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + r = -13.341664064 + -10 Combine like terms: 10 + -10 = 0 0 + r = -13.341664064 + -10 r = -13.341664064 + -10 Combine like terms: -13.341664064 + -10 = -23.341664064 r = -23.341664064 Simplifying r = -23.341664064Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.341664064, -23.341664064}
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