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Simplifying 10r2 + -21r = -4 + 6 Reorder the terms: -21r + 10r2 = -4 + 6 Combine like terms: -4 + 6 = 2 -21r + 10r2 = 2 Solving -21r + 10r2 = 2 Solving for variable 'r'. Reorder the terms: -2 + -21r + 10r2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -21r + 10r2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -2.1r + r2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -2.1r + 0.2 + r2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -2.1r + r2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -2.1r + r2 = 0 + 0.2 -2.1r + r2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -2.1r + r2 = 0.2 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 = 0.2 + 1.1025 Reorder the terms: 1.1025 + -2.1r + r2 = 0.2 + 1.1025 Combine like terms: 0.2 + 1.1025 = 1.3025 1.1025 + -2.1r + r2 = 1.3025 Factor a perfect square on the left side: (r + -1.05)(r + -1.05) = 1.3025 Calculate the square root of the right side: 1.141271221 Break this problem into two subproblems by setting (r + -1.05) equal to 1.141271221 and -1.141271221.Subproblem 1
r + -1.05 = 1.141271221 Simplifying r + -1.05 = 1.141271221 Reorder the terms: -1.05 + r = 1.141271221 Solving -1.05 + r = 1.141271221 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 = 1.141271221 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + r = 1.141271221 + 1.05 r = 1.141271221 + 1.05 Combine like terms: 1.141271221 + 1.05 = 2.191271221 r = 2.191271221 Simplifying r = 2.191271221Subproblem 2
r + -1.05 = -1.141271221 Simplifying r + -1.05 = -1.141271221 Reorder the terms: -1.05 + r = -1.141271221 Solving -1.05 + r = -1.141271221 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 = -1.141271221 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + r = -1.141271221 + 1.05 r = -1.141271221 + 1.05 Combine like terms: -1.141271221 + 1.05 = -0.091271221 r = -0.091271221 Simplifying r = -0.091271221Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.191271221, -0.091271221}
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