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Simplifying v2 + -42 = -35v Reorder the terms: -42 + v2 = -35v Solving -42 + v2 = -35v Solving for variable 'v'. Reorder the terms: -42 + 35v + v2 = -35v + 35v Combine like terms: -35v + 35v = 0 -42 + 35v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 35v + 42 + v2 = 0 + 42 Reorder the terms: -42 + 42 + 35v + v2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 35v + v2 = 0 + 42 35v + v2 = 0 + 42 Combine like terms: 0 + 42 = 42 35v + v2 = 42 The v term is 35v. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35v + 306.25 + v2 = 42 + 306.25 Reorder the terms: 306.25 + 35v + v2 = 42 + 306.25 Combine like terms: 42 + 306.25 = 348.25 306.25 + 35v + v2 = 348.25 Factor a perfect square on the left side: (v + 17.5)(v + 17.5) = 348.25 Calculate the square root of the right side: 18.661457607 Break this problem into two subproblems by setting (v + 17.5) equal to 18.661457607 and -18.661457607.Subproblem 1
v + 17.5 = 18.661457607 Simplifying v + 17.5 = 18.661457607 Reorder the terms: 17.5 + v = 18.661457607 Solving 17.5 + v = 18.661457607 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + v = 18.661457607 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + v = 18.661457607 + -17.5 v = 18.661457607 + -17.5 Combine like terms: 18.661457607 + -17.5 = 1.161457607 v = 1.161457607 Simplifying v = 1.161457607Subproblem 2
v + 17.5 = -18.661457607 Simplifying v + 17.5 = -18.661457607 Reorder the terms: 17.5 + v = -18.661457607 Solving 17.5 + v = -18.661457607 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + v = -18.661457607 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + v = -18.661457607 + -17.5 v = -18.661457607 + -17.5 Combine like terms: -18.661457607 + -17.5 = -36.161457607 v = -36.161457607 Simplifying v = -36.161457607Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.161457607, -36.161457607}
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