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Simplifying 5r2 + 3r = 14.81 Reorder the terms: 3r + 5r2 = 14.81 Solving 3r + 5r2 = 14.81 Solving for variable 'r'. Reorder the terms: -14.81 + 3r + 5r2 = 14.81 + -14.81 Combine like terms: 14.81 + -14.81 = 0.00 -14.81 + 3r + 5r2 = 0.00 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.962 + 0.6r + r2 = 0.00 Move the constant term to the right: Add '2.962' to each side of the equation. -2.962 + 0.6r + 2.962 + r2 = 0.00 + 2.962 Reorder the terms: -2.962 + 2.962 + 0.6r + r2 = 0.00 + 2.962 Combine like terms: -2.962 + 2.962 = 0.000 0.000 + 0.6r + r2 = 0.00 + 2.962 0.6r + r2 = 0.00 + 2.962 Combine like terms: 0.00 + 2.962 = 2.962 0.6r + r2 = 2.962 The r term is 0.6r. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6r + 0.09 + r2 = 2.962 + 0.09 Reorder the terms: 0.09 + 0.6r + r2 = 2.962 + 0.09 Combine like terms: 2.962 + 0.09 = 3.052 0.09 + 0.6r + r2 = 3.052 Factor a perfect square on the left side: (r + 0.3)(r + 0.3) = 3.052 Calculate the square root of the right side: 1.746997424 Break this problem into two subproblems by setting (r + 0.3) equal to 1.746997424 and -1.746997424.Subproblem 1
r + 0.3 = 1.746997424 Simplifying r + 0.3 = 1.746997424 Reorder the terms: 0.3 + r = 1.746997424 Solving 0.3 + r = 1.746997424 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + r = 1.746997424 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + r = 1.746997424 + -0.3 r = 1.746997424 + -0.3 Combine like terms: 1.746997424 + -0.3 = 1.446997424 r = 1.446997424 Simplifying r = 1.446997424Subproblem 2
r + 0.3 = -1.746997424 Simplifying r + 0.3 = -1.746997424 Reorder the terms: 0.3 + r = -1.746997424 Solving 0.3 + r = -1.746997424 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + r = -1.746997424 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + r = -1.746997424 + -0.3 r = -1.746997424 + -0.3 Combine like terms: -1.746997424 + -0.3 = -2.046997424 r = -2.046997424 Simplifying r = -2.046997424Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.446997424, -2.046997424}
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