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Simplifying 96.3r2 + 96.3r + -29.6 = 0 Reorder the terms: -29.6 + 96.3r + 96.3r2 = 0 Solving -29.6 + 96.3r + 96.3r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 96.3 the coefficient of the squared term: Divide each side by '96.3'. -0.3073727934 + r + r2 = 0 Move the constant term to the right: Add '0.3073727934' to each side of the equation. -0.3073727934 + r + 0.3073727934 + r2 = 0 + 0.3073727934 Reorder the terms: -0.3073727934 + 0.3073727934 + r + r2 = 0 + 0.3073727934 Combine like terms: -0.3073727934 + 0.3073727934 = 0.0000000000 0.0000000000 + r + r2 = 0 + 0.3073727934 r + r2 = 0 + 0.3073727934 Combine like terms: 0 + 0.3073727934 = 0.3073727934 r + r2 = 0.3073727934 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + r2 = 0.3073727934 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = 0.3073727934 + 0.25 Combine like terms: 0.3073727934 + 0.25 = 0.5573727934 1.25 + r2 = 0.5573727934 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 0.5573727934 Calculate the square root of the right side: 0.746574037 Break this problem into two subproblems by setting (r + 0.5) equal to 0.746574037 and -0.746574037.Subproblem 1
r + 0.5 = 0.746574037 Simplifying r + 0.5 = 0.746574037 Reorder the terms: 0.5 + r = 0.746574037 Solving 0.5 + r = 0.746574037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 0.746574037 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 0.746574037 + -0.5 r = 0.746574037 + -0.5 Combine like terms: 0.746574037 + -0.5 = 0.246574037 r = 0.246574037 Simplifying r = 0.246574037Subproblem 2
r + 0.5 = -0.746574037 Simplifying r + 0.5 = -0.746574037 Reorder the terms: 0.5 + r = -0.746574037 Solving 0.5 + r = -0.746574037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -0.746574037 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -0.746574037 + -0.5 r = -0.746574037 + -0.5 Combine like terms: -0.746574037 + -0.5 = -1.246574037 r = -1.246574037 Simplifying r = -1.246574037Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.246574037, -1.246574037}
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