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Simplifying v2 + -16v = 32 Reorder the terms: -16v + v2 = 32 Solving -16v + v2 = 32 Solving for variable 'v'. Reorder the terms: -32 + -16v + v2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -16v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -16v + 32 + v2 = 0 + 32 Reorder the terms: -32 + 32 + -16v + v2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -16v + v2 = 0 + 32 -16v + v2 = 0 + 32 Combine like terms: 0 + 32 = 32 -16v + v2 = 32 The v term is -16v. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16v + 64 + v2 = 32 + 64 Reorder the terms: 64 + -16v + v2 = 32 + 64 Combine like terms: 32 + 64 = 96 64 + -16v + v2 = 96 Factor a perfect square on the left side: (v + -8)(v + -8) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (v + -8) equal to 9.797958971 and -9.797958971.Subproblem 1
v + -8 = 9.797958971 Simplifying v + -8 = 9.797958971 Reorder the terms: -8 + v = 9.797958971 Solving -8 + v = 9.797958971 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + v = 9.797958971 + 8 Combine like terms: -8 + 8 = 0 0 + v = 9.797958971 + 8 v = 9.797958971 + 8 Combine like terms: 9.797958971 + 8 = 17.797958971 v = 17.797958971 Simplifying v = 17.797958971Subproblem 2
v + -8 = -9.797958971 Simplifying v + -8 = -9.797958971 Reorder the terms: -8 + v = -9.797958971 Solving -8 + v = -9.797958971 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + v = -9.797958971 + 8 Combine like terms: -8 + 8 = 0 0 + v = -9.797958971 + 8 v = -9.797958971 + 8 Combine like terms: -9.797958971 + 8 = -1.797958971 v = -1.797958971 Simplifying v = -1.797958971Solution
The solution to the problem is based on the solutions from the subproblems. v = {17.797958971, -1.797958971}
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