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Simplifying R2 + -18R + -29 = 8 Reorder the terms: -29 + -18R + R2 = 8 Solving -29 + -18R + R2 = 8 Solving for variable 'R'. Reorder the terms: -29 + -8 + -18R + R2 = 8 + -8 Combine like terms: -29 + -8 = -37 -37 + -18R + R2 = 8 + -8 Combine like terms: 8 + -8 = 0 -37 + -18R + R2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -18R + 37 + R2 = 0 + 37 Reorder the terms: -37 + 37 + -18R + R2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -18R + R2 = 0 + 37 -18R + R2 = 0 + 37 Combine like terms: 0 + 37 = 37 -18R + R2 = 37 The R term is -18R. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18R + 81 + R2 = 37 + 81 Reorder the terms: 81 + -18R + R2 = 37 + 81 Combine like terms: 37 + 81 = 118 81 + -18R + R2 = 118 Factor a perfect square on the left side: (R + -9)(R + -9) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (R + -9) equal to 10.862780491 and -10.862780491.Subproblem 1
R + -9 = 10.862780491 Simplifying R + -9 = 10.862780491 Reorder the terms: -9 + R = 10.862780491 Solving -9 + R = 10.862780491 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + R = 10.862780491 + 9 Combine like terms: -9 + 9 = 0 0 + R = 10.862780491 + 9 R = 10.862780491 + 9 Combine like terms: 10.862780491 + 9 = 19.862780491 R = 19.862780491 Simplifying R = 19.862780491Subproblem 2
R + -9 = -10.862780491 Simplifying R + -9 = -10.862780491 Reorder the terms: -9 + R = -10.862780491 Solving -9 + R = -10.862780491 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + R = -10.862780491 + 9 Combine like terms: -9 + 9 = 0 0 + R = -10.862780491 + 9 R = -10.862780491 + 9 Combine like terms: -10.862780491 + 9 = -1.862780491 R = -1.862780491 Simplifying R = -1.862780491Solution
The solution to the problem is based on the solutions from the subproblems. R = {19.862780491, -1.862780491}
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