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Simplifying 3v2 + 14.28453709v = 255.06 Reorder the terms: 14.28453709v + 3v2 = 255.06 Solving 14.28453709v + 3v2 = 255.06 Solving for variable 'v'. Reorder the terms: -255.06 + 14.28453709v + 3v2 = 255.06 + -255.06 Combine like terms: 255.06 + -255.06 = 0.00 -255.06 + 14.28453709v + 3v2 = 0.00 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -85.02 + 4.761512363v + v2 = 0.00 Move the constant term to the right: Add '85.02' to each side of the equation. -85.02 + 4.761512363v + 85.02 + v2 = 0.00 + 85.02 Reorder the terms: -85.02 + 85.02 + 4.761512363v + v2 = 0.00 + 85.02 Combine like terms: -85.02 + 85.02 = 0.00 0.00 + 4.761512363v + v2 = 0.00 + 85.02 4.761512363v + v2 = 0.00 + 85.02 Combine like terms: 0.00 + 85.02 = 85.02 4.761512363v + v2 = 85.02 The v term is 4.761512363v. Take half its coefficient (2.380756182). Square it (5.667999998) and add it to both sides. Add '5.667999998' to each side of the equation. 4.761512363v + 5.667999998 + v2 = 85.02 + 5.667999998 Reorder the terms: 5.667999998 + 4.761512363v + v2 = 85.02 + 5.667999998 Combine like terms: 85.02 + 5.667999998 = 90.687999998 5.667999998 + 4.761512363v + v2 = 90.687999998 Factor a perfect square on the left side: (v + 2.380756182)(v + 2.380756182) = 90.687999998 Calculate the square root of the right side: 9.523024729 Break this problem into two subproblems by setting (v + 2.380756182) equal to 9.523024729 and -9.523024729.Subproblem 1
v + 2.380756182 = 9.523024729 Simplifying v + 2.380756182 = 9.523024729 Reorder the terms: 2.380756182 + v = 9.523024729 Solving 2.380756182 + v = 9.523024729 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.380756182' to each side of the equation. 2.380756182 + -2.380756182 + v = 9.523024729 + -2.380756182 Combine like terms: 2.380756182 + -2.380756182 = 0.000000000 0.000000000 + v = 9.523024729 + -2.380756182 v = 9.523024729 + -2.380756182 Combine like terms: 9.523024729 + -2.380756182 = 7.142268547 v = 7.142268547 Simplifying v = 7.142268547Subproblem 2
v + 2.380756182 = -9.523024729 Simplifying v + 2.380756182 = -9.523024729 Reorder the terms: 2.380756182 + v = -9.523024729 Solving 2.380756182 + v = -9.523024729 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.380756182' to each side of the equation. 2.380756182 + -2.380756182 + v = -9.523024729 + -2.380756182 Combine like terms: 2.380756182 + -2.380756182 = 0.000000000 0.000000000 + v = -9.523024729 + -2.380756182 v = -9.523024729 + -2.380756182 Combine like terms: -9.523024729 + -2.380756182 = -11.903780911 v = -11.903780911 Simplifying v = -11.903780911Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.142268547, -11.903780911}
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