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Simplifying v2 + 33v + -15 = 0 Reorder the terms: -15 + 33v + v2 = 0 Solving -15 + 33v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 33v + 15 + v2 = 0 + 15 Reorder the terms: -15 + 15 + 33v + v2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 33v + v2 = 0 + 15 33v + v2 = 0 + 15 Combine like terms: 0 + 15 = 15 33v + v2 = 15 The v term is 33v. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33v + 272.25 + v2 = 15 + 272.25 Reorder the terms: 272.25 + 33v + v2 = 15 + 272.25 Combine like terms: 15 + 272.25 = 287.25 272.25 + 33v + v2 = 287.25 Factor a perfect square on the left side: (v + 16.5)(v + 16.5) = 287.25 Calculate the square root of the right side: 16.948451257 Break this problem into two subproblems by setting (v + 16.5) equal to 16.948451257 and -16.948451257.Subproblem 1
v + 16.5 = 16.948451257 Simplifying v + 16.5 = 16.948451257 Reorder the terms: 16.5 + v = 16.948451257 Solving 16.5 + v = 16.948451257 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + v = 16.948451257 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + v = 16.948451257 + -16.5 v = 16.948451257 + -16.5 Combine like terms: 16.948451257 + -16.5 = 0.448451257 v = 0.448451257 Simplifying v = 0.448451257Subproblem 2
v + 16.5 = -16.948451257 Simplifying v + 16.5 = -16.948451257 Reorder the terms: 16.5 + v = -16.948451257 Solving 16.5 + v = -16.948451257 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + v = -16.948451257 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + v = -16.948451257 + -16.5 v = -16.948451257 + -16.5 Combine like terms: -16.948451257 + -16.5 = -33.448451257 v = -33.448451257 Simplifying v = -33.448451257Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.448451257, -33.448451257}
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