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Simplifying v2 + -16v = 98 Reorder the terms: -16v + v2 = 98 Solving -16v + v2 = 98 Solving for variable 'v'. Reorder the terms: -98 + -16v + v2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + -16v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -16v + 98 + v2 = 0 + 98 Reorder the terms: -98 + 98 + -16v + v2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -16v + v2 = 0 + 98 -16v + v2 = 0 + 98 Combine like terms: 0 + 98 = 98 -16v + v2 = 98 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 = 98 + 64 Reorder the terms: 64 + -16v + v2 = 98 + 64 Combine like terms: 98 + 64 = 162 64 + -16v + v2 = 162 Factor a perfect square on the left side: (v + -8)(v + -8) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (v + -8) equal to 12.727922061 and -12.727922061.Subproblem 1
v + -8 = 12.727922061 Simplifying v + -8 = 12.727922061 Reorder the terms: -8 + v = 12.727922061 Solving -8 + v = 12.727922061 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 = 12.727922061 + 8 Combine like terms: -8 + 8 = 0 0 + v = 12.727922061 + 8 v = 12.727922061 + 8 Combine like terms: 12.727922061 + 8 = 20.727922061 v = 20.727922061 Simplifying v = 20.727922061Subproblem 2
v + -8 = -12.727922061 Simplifying v + -8 = -12.727922061 Reorder the terms: -8 + v = -12.727922061 Solving -8 + v = -12.727922061 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 = -12.727922061 + 8 Combine like terms: -8 + 8 = 0 0 + v = -12.727922061 + 8 v = -12.727922061 + 8 Combine like terms: -12.727922061 + 8 = -4.727922061 v = -4.727922061 Simplifying v = -4.727922061Solution
The solution to the problem is based on the solutions from the subproblems. v = {20.727922061, -4.727922061}
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