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Simplifying 8r2 + -17 = 3r Reorder the terms: -17 + 8r2 = 3r Solving -17 + 8r2 = 3r Solving for variable 'r'. Reorder the terms: -17 + -3r + 8r2 = 3r + -3r Combine like terms: 3r + -3r = 0 -17 + -3r + 8r2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + -0.375r + r2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + -0.375r + 2.125 + r2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + -0.375r + r2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + -0.375r + r2 = 0 + 2.125 -0.375r + r2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 -0.375r + r2 = 2.125 The r term is -0.375r. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375r + 0.03515625 + r2 = 2.125 + 0.03515625 Reorder the terms: 0.03515625 + -0.375r + r2 = 2.125 + 0.03515625 Combine like terms: 2.125 + 0.03515625 = 2.16015625 0.03515625 + -0.375r + r2 = 2.16015625 Factor a perfect square on the left side: (r + -0.1875)(r + -0.1875) = 2.16015625 Calculate the square root of the right side: 1.469747002 Break this problem into two subproblems by setting (r + -0.1875) equal to 1.469747002 and -1.469747002.Subproblem 1
r + -0.1875 = 1.469747002 Simplifying r + -0.1875 = 1.469747002 Reorder the terms: -0.1875 + r = 1.469747002 Solving -0.1875 + r = 1.469747002 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + r = 1.469747002 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + r = 1.469747002 + 0.1875 r = 1.469747002 + 0.1875 Combine like terms: 1.469747002 + 0.1875 = 1.657247002 r = 1.657247002 Simplifying r = 1.657247002Subproblem 2
r + -0.1875 = -1.469747002 Simplifying r + -0.1875 = -1.469747002 Reorder the terms: -0.1875 + r = -1.469747002 Solving -0.1875 + r = -1.469747002 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + r = -1.469747002 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + r = -1.469747002 + 0.1875 r = -1.469747002 + 0.1875 Combine like terms: -1.469747002 + 0.1875 = -1.282247002 r = -1.282247002 Simplifying r = -1.282247002Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.657247002, -1.282247002}
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