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Simplifying 48r = 9 + r2 Solving 48r = 9 + r2 Solving for variable 'r'. Reorder the terms: -9 + 48r + -1r2 = 9 + r2 + -9 + -1r2 Reorder the terms: -9 + 48r + -1r2 = 9 + -9 + r2 + -1r2 Combine like terms: 9 + -9 = 0 -9 + 48r + -1r2 = 0 + r2 + -1r2 -9 + 48r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -9 + 48r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -48r + r2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -48r + -9 + r2 = 0 + -9 Reorder the terms: 9 + -9 + -48r + r2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -48r + r2 = 0 + -9 -48r + r2 = 0 + -9 Combine like terms: 0 + -9 = -9 -48r + r2 = -9 The r term is -48r. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48r + 576 + r2 = -9 + 576 Reorder the terms: 576 + -48r + r2 = -9 + 576 Combine like terms: -9 + 576 = 567 576 + -48r + r2 = 567 Factor a perfect square on the left side: (r + -24)(r + -24) = 567 Calculate the square root of the right side: 23.8117618 Break this problem into two subproblems by setting (r + -24) equal to 23.8117618 and -23.8117618.Subproblem 1
r + -24 = 23.8117618 Simplifying r + -24 = 23.8117618 Reorder the terms: -24 + r = 23.8117618 Solving -24 + r = 23.8117618 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + r = 23.8117618 + 24 Combine like terms: -24 + 24 = 0 0 + r = 23.8117618 + 24 r = 23.8117618 + 24 Combine like terms: 23.8117618 + 24 = 47.8117618 r = 47.8117618 Simplifying r = 47.8117618Subproblem 2
r + -24 = -23.8117618 Simplifying r + -24 = -23.8117618 Reorder the terms: -24 + r = -23.8117618 Solving -24 + r = -23.8117618 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + r = -23.8117618 + 24 Combine like terms: -24 + 24 = 0 0 + r = -23.8117618 + 24 r = -23.8117618 + 24 Combine like terms: -23.8117618 + 24 = 0.1882382 r = 0.1882382 Simplifying r = 0.1882382Solution
The solution to the problem is based on the solutions from the subproblems. r = {47.8117618, 0.1882382}
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