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Simplifying 4r2 + 17r + -18 = 0 Reorder the terms: -18 + 17r + 4r2 = 0 Solving -18 + 17r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 4.25r + r2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 4.25r + 4.5 + r2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 4.25r + r2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 4.25r + r2 = 0 + 4.5 4.25r + r2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 4.25r + r2 = 4.5 The r term is 4.25r. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25r + 4.515625 + r2 = 4.5 + 4.515625 Reorder the terms: 4.515625 + 4.25r + r2 = 4.5 + 4.515625 Combine like terms: 4.5 + 4.515625 = 9.015625 4.515625 + 4.25r + r2 = 9.015625 Factor a perfect square on the left side: (r + 2.125)(r + 2.125) = 9.015625 Calculate the square root of the right side: 3.002603037 Break this problem into two subproblems by setting (r + 2.125) equal to 3.002603037 and -3.002603037.Subproblem 1
r + 2.125 = 3.002603037 Simplifying r + 2.125 = 3.002603037 Reorder the terms: 2.125 + r = 3.002603037 Solving 2.125 + r = 3.002603037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + r = 3.002603037 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + r = 3.002603037 + -2.125 r = 3.002603037 + -2.125 Combine like terms: 3.002603037 + -2.125 = 0.877603037 r = 0.877603037 Simplifying r = 0.877603037Subproblem 2
r + 2.125 = -3.002603037 Simplifying r + 2.125 = -3.002603037 Reorder the terms: 2.125 + r = -3.002603037 Solving 2.125 + r = -3.002603037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + r = -3.002603037 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + r = -3.002603037 + -2.125 r = -3.002603037 + -2.125 Combine like terms: -3.002603037 + -2.125 = -5.127603037 r = -5.127603037 Simplifying r = -5.127603037Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.877603037, -5.127603037}
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