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Simplifying -8r2 + 64r + 19 = 0 Reorder the terms: 19 + 64r + -8r2 = 0 Solving 19 + 64r + -8r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.375 + -8r + r2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -8r + 2.375 + r2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -8r + r2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -8r + r2 = 0 + 2.375 -8r + r2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -8r + r2 = 2.375 The r term is -8r. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8r + 16 + r2 = 2.375 + 16 Reorder the terms: 16 + -8r + r2 = 2.375 + 16 Combine like terms: 2.375 + 16 = 18.375 16 + -8r + r2 = 18.375 Factor a perfect square on the left side: (r + -4)(r + -4) = 18.375 Calculate the square root of the right side: 4.28660705 Break this problem into two subproblems by setting (r + -4) equal to 4.28660705 and -4.28660705.Subproblem 1
r + -4 = 4.28660705 Simplifying r + -4 = 4.28660705 Reorder the terms: -4 + r = 4.28660705 Solving -4 + r = 4.28660705 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 4.28660705 + 4 Combine like terms: -4 + 4 = 0 0 + r = 4.28660705 + 4 r = 4.28660705 + 4 Combine like terms: 4.28660705 + 4 = 8.28660705 r = 8.28660705 Simplifying r = 8.28660705Subproblem 2
r + -4 = -4.28660705 Simplifying r + -4 = -4.28660705 Reorder the terms: -4 + r = -4.28660705 Solving -4 + r = -4.28660705 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = -4.28660705 + 4 Combine like terms: -4 + 4 = 0 0 + r = -4.28660705 + 4 r = -4.28660705 + 4 Combine like terms: -4.28660705 + 4 = -0.28660705 r = -0.28660705 Simplifying r = -0.28660705Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.28660705, -0.28660705}
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