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Simplifying 5r2 + -48r + 20 = 0 Reorder the terms: 20 + -48r + 5r2 = 0 Solving 20 + -48r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -9.6r + r2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -9.6r + -4 + r2 = 0 + -4 Reorder the terms: 4 + -4 + -9.6r + r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9.6r + r2 = 0 + -4 -9.6r + r2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9.6r + r2 = -4 The r term is -9.6r. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6r + 23.04 + r2 = -4 + 23.04 Reorder the terms: 23.04 + -9.6r + r2 = -4 + 23.04 Combine like terms: -4 + 23.04 = 19.04 23.04 + -9.6r + r2 = 19.04 Factor a perfect square on the left side: (r + -4.8)(r + -4.8) = 19.04 Calculate the square root of the right side: 4.363484846 Break this problem into two subproblems by setting (r + -4.8) equal to 4.363484846 and -4.363484846.Subproblem 1
r + -4.8 = 4.363484846 Simplifying r + -4.8 = 4.363484846 Reorder the terms: -4.8 + r = 4.363484846 Solving -4.8 + r = 4.363484846 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + r = 4.363484846 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + r = 4.363484846 + 4.8 r = 4.363484846 + 4.8 Combine like terms: 4.363484846 + 4.8 = 9.163484846 r = 9.163484846 Simplifying r = 9.163484846Subproblem 2
r + -4.8 = -4.363484846 Simplifying r + -4.8 = -4.363484846 Reorder the terms: -4.8 + r = -4.363484846 Solving -4.8 + r = -4.363484846 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + r = -4.363484846 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + r = -4.363484846 + 4.8 r = -4.363484846 + 4.8 Combine like terms: -4.363484846 + 4.8 = 0.436515154 r = 0.436515154 Simplifying r = 0.436515154Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.163484846, 0.436515154}
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