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Simplifying 16r2 + -55r + -96 = 0 Reorder the terms: -96 + -55r + 16r2 = 0 Solving -96 + -55r + 16r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6 + -3.4375r + r2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3.4375r + 6 + r2 = 0 + 6 Reorder the terms: -6 + 6 + -3.4375r + r2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3.4375r + r2 = 0 + 6 -3.4375r + r2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3.4375r + r2 = 6 The r term is -3.4375r. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375r + 2.954101563 + r2 = 6 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375r + r2 = 6 + 2.954101563 Combine like terms: 6 + 2.954101563 = 8.954101563 2.954101563 + -3.4375r + r2 = 8.954101563 Factor a perfect square on the left side: (r + -1.71875)(r + -1.71875) = 8.954101563 Calculate the square root of the right side: 2.992340482 Break this problem into two subproblems by setting (r + -1.71875) equal to 2.992340482 and -2.992340482.Subproblem 1
r + -1.71875 = 2.992340482 Simplifying r + -1.71875 = 2.992340482 Reorder the terms: -1.71875 + r = 2.992340482 Solving -1.71875 + r = 2.992340482 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + r = 2.992340482 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + r = 2.992340482 + 1.71875 r = 2.992340482 + 1.71875 Combine like terms: 2.992340482 + 1.71875 = 4.711090482 r = 4.711090482 Simplifying r = 4.711090482Subproblem 2
r + -1.71875 = -2.992340482 Simplifying r + -1.71875 = -2.992340482 Reorder the terms: -1.71875 + r = -2.992340482 Solving -1.71875 + r = -2.992340482 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + r = -2.992340482 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + r = -2.992340482 + 1.71875 r = -2.992340482 + 1.71875 Combine like terms: -2.992340482 + 1.71875 = -1.273590482 r = -1.273590482 Simplifying r = -1.273590482Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.711090482, -1.273590482}
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