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Simplifying 29r = 3(r2 + 4) Reorder the terms: 29r = 3(4 + r2) 29r = (4 * 3 + r2 * 3) 29r = (12 + 3r2) Solving 29r = 12 + 3r2 Solving for variable 'r'. Reorder the terms: -12 + 29r + -3r2 = 12 + 3r2 + -12 + -3r2 Reorder the terms: -12 + 29r + -3r2 = 12 + -12 + 3r2 + -3r2 Combine like terms: 12 + -12 = 0 -12 + 29r + -3r2 = 0 + 3r2 + -3r2 -12 + 29r + -3r2 = 3r2 + -3r2 Combine like terms: 3r2 + -3r2 = 0 -12 + 29r + -3r2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 4 + -9.666666667r + r2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -9.666666667r + -4 + r2 = 0 + -4 Reorder the terms: 4 + -4 + -9.666666667r + r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9.666666667r + r2 = 0 + -4 -9.666666667r + r2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9.666666667r + r2 = -4 The r term is -9.666666667r. Take half its coefficient (-4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. -9.666666667r + 23.36111112 + r2 = -4 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667r + r2 = -4 + 23.36111112 Combine like terms: -4 + 23.36111112 = 19.36111112 23.36111112 + -9.666666667r + r2 = 19.36111112 Factor a perfect square on the left side: (r + -4.833333334)(r + -4.833333334) = 19.36111112 Calculate the square root of the right side: 4.400126262 Break this problem into two subproblems by setting (r + -4.833333334) equal to 4.400126262 and -4.400126262.Subproblem 1
r + -4.833333334 = 4.400126262 Simplifying r + -4.833333334 = 4.400126262 Reorder the terms: -4.833333334 + r = 4.400126262 Solving -4.833333334 + r = 4.400126262 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + r = 4.400126262 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + r = 4.400126262 + 4.833333334 r = 4.400126262 + 4.833333334 Combine like terms: 4.400126262 + 4.833333334 = 9.233459596 r = 9.233459596 Simplifying r = 9.233459596Subproblem 2
r + -4.833333334 = -4.400126262 Simplifying r + -4.833333334 = -4.400126262 Reorder the terms: -4.833333334 + r = -4.400126262 Solving -4.833333334 + r = -4.400126262 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + r = -4.400126262 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + r = -4.400126262 + 4.833333334 r = -4.400126262 + 4.833333334 Combine like terms: -4.400126262 + 4.833333334 = 0.433207072 r = 0.433207072 Simplifying r = 0.433207072Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.233459596, 0.433207072}
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