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Simplifying 79430.28 = r(629.4 + -1r) 79430.28 = (629.4 * r + -1r * r) 79430.28 = (629.4r + -1r2) Solving 79430.28 = 629.4r + -1r2 Solving for variable 'r'. Reorder the terms: 79430.28 + -629.4r + r2 = 629.4r + -629.4r + -1r2 + r2 Combine like terms: 629.4r + -629.4r = 0.0 79430.28 + -629.4r + r2 = 0.0 + -1r2 + r2 79430.28 + -629.4r + r2 = -1r2 + r2 Combine like terms: -1r2 + r2 = 0 79430.28 + -629.4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-79430.28' to each side of the equation. 79430.28 + -629.4r + -79430.28 + r2 = 0 + -79430.28 Reorder the terms: 79430.28 + -79430.28 + -629.4r + r2 = 0 + -79430.28 Combine like terms: 79430.28 + -79430.28 = 0.00 0.00 + -629.4r + r2 = 0 + -79430.28 -629.4r + r2 = 0 + -79430.28 Combine like terms: 0 + -79430.28 = -79430.28 -629.4r + r2 = -79430.28 The r term is -629.4r. Take half its coefficient (-314.7). Square it (99036.09) and add it to both sides. Add '99036.09' to each side of the equation. -629.4r + 99036.09 + r2 = -79430.28 + 99036.09 Reorder the terms: 99036.09 + -629.4r + r2 = -79430.28 + 99036.09 Combine like terms: -79430.28 + 99036.09 = 19605.81 99036.09 + -629.4r + r2 = 19605.81 Factor a perfect square on the left side: (r + -314.7)(r + -314.7) = 19605.81 Calculate the square root of the right side: 140.020748463 Break this problem into two subproblems by setting (r + -314.7) equal to 140.020748463 and -140.020748463.Subproblem 1
r + -314.7 = 140.020748463 Simplifying r + -314.7 = 140.020748463 Reorder the terms: -314.7 + r = 140.020748463 Solving -314.7 + r = 140.020748463 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '314.7' to each side of the equation. -314.7 + 314.7 + r = 140.020748463 + 314.7 Combine like terms: -314.7 + 314.7 = 0.0 0.0 + r = 140.020748463 + 314.7 r = 140.020748463 + 314.7 Combine like terms: 140.020748463 + 314.7 = 454.720748463 r = 454.720748463 Simplifying r = 454.720748463Subproblem 2
r + -314.7 = -140.020748463 Simplifying r + -314.7 = -140.020748463 Reorder the terms: -314.7 + r = -140.020748463 Solving -314.7 + r = -140.020748463 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '314.7' to each side of the equation. -314.7 + 314.7 + r = -140.020748463 + 314.7 Combine like terms: -314.7 + 314.7 = 0.0 0.0 + r = -140.020748463 + 314.7 r = -140.020748463 + 314.7 Combine like terms: -140.020748463 + 314.7 = 174.679251537 r = 174.679251537 Simplifying r = 174.679251537Solution
The solution to the problem is based on the solutions from the subproblems. r = {454.720748463, 174.679251537}
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