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Simplifying (-9r2 + 8r + 8) + -1(8r2 + 10r + -2) = 0 Reorder the terms: (8 + 8r + -9r2) + -1(8r2 + 10r + -2) = 0 Remove parenthesis around (8 + 8r + -9r2) 8 + 8r + -9r2 + -1(8r2 + 10r + -2) = 0 Reorder the terms: 8 + 8r + -9r2 + -1(-2 + 10r + 8r2) = 0 8 + 8r + -9r2 + (-2 * -1 + 10r * -1 + 8r2 * -1) = 0 8 + 8r + -9r2 + (2 + -10r + -8r2) = 0 Reorder the terms: 8 + 2 + 8r + -10r + -9r2 + -8r2 = 0 Combine like terms: 8 + 2 = 10 10 + 8r + -10r + -9r2 + -8r2 = 0 Combine like terms: 8r + -10r = -2r 10 + -2r + -9r2 + -8r2 = 0 Combine like terms: -9r2 + -8r2 = -17r2 10 + -2r + -17r2 = 0 Solving 10 + -2r + -17r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -0.5882352941 + 0.1176470588r + r2 = 0 Move the constant term to the right: Add '0.5882352941' to each side of the equation. -0.5882352941 + 0.1176470588r + 0.5882352941 + r2 = 0 + 0.5882352941 Reorder the terms: -0.5882352941 + 0.5882352941 + 0.1176470588r + r2 = 0 + 0.5882352941 Combine like terms: -0.5882352941 + 0.5882352941 = 0.0000000000 0.0000000000 + 0.1176470588r + r2 = 0 + 0.5882352941 0.1176470588r + r2 = 0 + 0.5882352941 Combine like terms: 0 + 0.5882352941 = 0.5882352941 0.1176470588r + r2 = 0.5882352941 The r term is 0.1176470588r. Take half its coefficient (0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. 0.1176470588r + 0.003460207611 + r2 = 0.5882352941 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588r + r2 = 0.5882352941 + 0.003460207611 Combine like terms: 0.5882352941 + 0.003460207611 = 0.591695501711 0.003460207611 + 0.1176470588r + r2 = 0.591695501711 Factor a perfect square on the left side: (r + 0.0588235294)(r + 0.0588235294) = 0.591695501711 Calculate the square root of the right side: 0.769217461 Break this problem into two subproblems by setting (r + 0.0588235294) equal to 0.769217461 and -0.769217461.Subproblem 1
r + 0.0588235294 = 0.769217461 Simplifying r + 0.0588235294 = 0.769217461 Reorder the terms: 0.0588235294 + r = 0.769217461 Solving 0.0588235294 + r = 0.769217461 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + r = 0.769217461 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + r = 0.769217461 + -0.0588235294 r = 0.769217461 + -0.0588235294 Combine like terms: 0.769217461 + -0.0588235294 = 0.7103939316 r = 0.7103939316 Simplifying r = 0.7103939316Subproblem 2
r + 0.0588235294 = -0.769217461 Simplifying r + 0.0588235294 = -0.769217461 Reorder the terms: 0.0588235294 + r = -0.769217461 Solving 0.0588235294 + r = -0.769217461 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + r = -0.769217461 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + r = -0.769217461 + -0.0588235294 r = -0.769217461 + -0.0588235294 Combine like terms: -0.769217461 + -0.0588235294 = -0.8280409904 r = -0.8280409904 Simplifying r = -0.8280409904Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.7103939316, -0.8280409904}
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