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Simplifying 9r2 + -8r + -16 = 5 Reorder the terms: -16 + -8r + 9r2 = 5 Solving -16 + -8r + 9r2 = 5 Solving for variable 'r'. Reorder the terms: -16 + -5 + -8r + 9r2 = 5 + -5 Combine like terms: -16 + -5 = -21 -21 + -8r + 9r2 = 5 + -5 Combine like terms: 5 + -5 = 0 -21 + -8r + 9r2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.333333333 + -0.8888888889r + r2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -0.8888888889r + 2.333333333 + r2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -0.8888888889r + r2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -0.8888888889r + r2 = 0 + 2.333333333 -0.8888888889r + r2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -0.8888888889r + r2 = 2.333333333 The r term is -0.8888888889r. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889r + 0.1975308642 + r2 = 2.333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889r + r2 = 2.333333333 + 0.1975308642 Combine like terms: 2.333333333 + 0.1975308642 = 2.5308641972 0.1975308642 + -0.8888888889r + r2 = 2.5308641972 Factor a perfect square on the left side: (r + -0.4444444445)(r + -0.4444444445) = 2.5308641972 Calculate the square root of the right side: 1.590869007 Break this problem into two subproblems by setting (r + -0.4444444445) equal to 1.590869007 and -1.590869007.Subproblem 1
r + -0.4444444445 = 1.590869007 Simplifying r + -0.4444444445 = 1.590869007 Reorder the terms: -0.4444444445 + r = 1.590869007 Solving -0.4444444445 + r = 1.590869007 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + r = 1.590869007 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + r = 1.590869007 + 0.4444444445 r = 1.590869007 + 0.4444444445 Combine like terms: 1.590869007 + 0.4444444445 = 2.0353134515 r = 2.0353134515 Simplifying r = 2.0353134515Subproblem 2
r + -0.4444444445 = -1.590869007 Simplifying r + -0.4444444445 = -1.590869007 Reorder the terms: -0.4444444445 + r = -1.590869007 Solving -0.4444444445 + r = -1.590869007 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + r = -1.590869007 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + r = -1.590869007 + 0.4444444445 r = -1.590869007 + 0.4444444445 Combine like terms: -1.590869007 + 0.4444444445 = -1.1464245625 r = -1.1464245625 Simplifying r = -1.1464245625Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.0353134515, -1.1464245625}
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