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Simplifying 7r2 + -14r + -87 = 9 Reorder the terms: -87 + -14r + 7r2 = 9 Solving -87 + -14r + 7r2 = 9 Solving for variable 'r'. Reorder the terms: -87 + -9 + -14r + 7r2 = 9 + -9 Combine like terms: -87 + -9 = -96 -96 + -14r + 7r2 = 9 + -9 Combine like terms: 9 + -9 = 0 -96 + -14r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -13.71428571 + -2r + r2 = 0 Move the constant term to the right: Add '13.71428571' to each side of the equation. -13.71428571 + -2r + 13.71428571 + r2 = 0 + 13.71428571 Reorder the terms: -13.71428571 + 13.71428571 + -2r + r2 = 0 + 13.71428571 Combine like terms: -13.71428571 + 13.71428571 = 0.00000000 0.00000000 + -2r + r2 = 0 + 13.71428571 -2r + r2 = 0 + 13.71428571 Combine like terms: 0 + 13.71428571 = 13.71428571 -2r + r2 = 13.71428571 The r term is -2r. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r + 1 + r2 = 13.71428571 + 1 Reorder the terms: 1 + -2r + r2 = 13.71428571 + 1 Combine like terms: 13.71428571 + 1 = 14.71428571 1 + -2r + r2 = 14.71428571 Factor a perfect square on the left side: (r + -1)(r + -1) = 14.71428571 Calculate the square root of the right side: 3.835920451 Break this problem into two subproblems by setting (r + -1) equal to 3.835920451 and -3.835920451.Subproblem 1
r + -1 = 3.835920451 Simplifying r + -1 = 3.835920451 Reorder the terms: -1 + r = 3.835920451 Solving -1 + r = 3.835920451 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 3.835920451 + 1 Combine like terms: -1 + 1 = 0 0 + r = 3.835920451 + 1 r = 3.835920451 + 1 Combine like terms: 3.835920451 + 1 = 4.835920451 r = 4.835920451 Simplifying r = 4.835920451Subproblem 2
r + -1 = -3.835920451 Simplifying r + -1 = -3.835920451 Reorder the terms: -1 + r = -3.835920451 Solving -1 + r = -3.835920451 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -3.835920451 + 1 Combine like terms: -1 + 1 = 0 0 + r = -3.835920451 + 1 r = -3.835920451 + 1 Combine like terms: -3.835920451 + 1 = -2.835920451 r = -2.835920451 Simplifying r = -2.835920451Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.835920451, -2.835920451}
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