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Simplifying 50r2 + 105r + -8 = 0 Reorder the terms: -8 + 105r + 50r2 = 0 Solving -8 + 105r + 50r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.16 + 2.1r + r2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + 2.1r + 0.16 + r2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + 2.1r + r2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + 2.1r + r2 = 0 + 0.16 2.1r + r2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 2.1r + r2 = 0.16 The r term is 2.1r. Take half its coefficient (1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. 2.1r + 1.1025 + r2 = 0.16 + 1.1025 Reorder the terms: 1.1025 + 2.1r + r2 = 0.16 + 1.1025 Combine like terms: 0.16 + 1.1025 = 1.2625 1.1025 + 2.1r + r2 = 1.2625 Factor a perfect square on the left side: (r + 1.05)(r + 1.05) = 1.2625 Calculate the square root of the right side: 1.123610253 Break this problem into two subproblems by setting (r + 1.05) equal to 1.123610253 and -1.123610253.Subproblem 1
r + 1.05 = 1.123610253 Simplifying r + 1.05 = 1.123610253 Reorder the terms: 1.05 + r = 1.123610253 Solving 1.05 + r = 1.123610253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + r = 1.123610253 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + r = 1.123610253 + -1.05 r = 1.123610253 + -1.05 Combine like terms: 1.123610253 + -1.05 = 0.073610253 r = 0.073610253 Simplifying r = 0.073610253Subproblem 2
r + 1.05 = -1.123610253 Simplifying r + 1.05 = -1.123610253 Reorder the terms: 1.05 + r = -1.123610253 Solving 1.05 + r = -1.123610253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + r = -1.123610253 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + r = -1.123610253 + -1.05 r = -1.123610253 + -1.05 Combine like terms: -1.123610253 + -1.05 = -2.173610253 r = -2.173610253 Simplifying r = -2.173610253Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.073610253, -2.173610253}
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