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Simplifying 4r2 + 24r = -17 Reorder the terms: 24r + 4r2 = -17 Solving 24r + 4r2 = -17 Solving for variable 'r'. Reorder the terms: 17 + 24r + 4r2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 24r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.25 + 6r + r2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + 6r + -4.25 + r2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + 6r + r2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + 6r + r2 = 0 + -4.25 6r + r2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 6r + r2 = -4.25 The r term is 6r. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6r + 9 + r2 = -4.25 + 9 Reorder the terms: 9 + 6r + r2 = -4.25 + 9 Combine like terms: -4.25 + 9 = 4.75 9 + 6r + r2 = 4.75 Factor a perfect square on the left side: (r + 3)(r + 3) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (r + 3) equal to 2.179449472 and -2.179449472.Subproblem 1
r + 3 = 2.179449472 Simplifying r + 3 = 2.179449472 Reorder the terms: 3 + r = 2.179449472 Solving 3 + r = 2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 2.179449472 + -3 Combine like terms: 3 + -3 = 0 0 + r = 2.179449472 + -3 r = 2.179449472 + -3 Combine like terms: 2.179449472 + -3 = -0.820550528 r = -0.820550528 Simplifying r = -0.820550528Subproblem 2
r + 3 = -2.179449472 Simplifying r + 3 = -2.179449472 Reorder the terms: 3 + r = -2.179449472 Solving 3 + r = -2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -2.179449472 + -3 Combine like terms: 3 + -3 = 0 0 + r = -2.179449472 + -3 r = -2.179449472 + -3 Combine like terms: -2.179449472 + -3 = -5.179449472 r = -5.179449472 Simplifying r = -5.179449472Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.820550528, -5.179449472}
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