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Simplifying v2 + -30v + 18 = 0 Reorder the terms: 18 + -30v + v2 = 0 Solving 18 + -30v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -30v + -18 + v2 = 0 + -18 Reorder the terms: 18 + -18 + -30v + v2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -30v + v2 = 0 + -18 -30v + v2 = 0 + -18 Combine like terms: 0 + -18 = -18 -30v + v2 = -18 The v term is -30v. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30v + 225 + v2 = -18 + 225 Reorder the terms: 225 + -30v + v2 = -18 + 225 Combine like terms: -18 + 225 = 207 225 + -30v + v2 = 207 Factor a perfect square on the left side: (v + -15)(v + -15) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (v + -15) equal to 14.38749457 and -14.38749457.Subproblem 1
v + -15 = 14.38749457 Simplifying v + -15 = 14.38749457 Reorder the terms: -15 + v = 14.38749457 Solving -15 + v = 14.38749457 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + v = 14.38749457 + 15 Combine like terms: -15 + 15 = 0 0 + v = 14.38749457 + 15 v = 14.38749457 + 15 Combine like terms: 14.38749457 + 15 = 29.38749457 v = 29.38749457 Simplifying v = 29.38749457Subproblem 2
v + -15 = -14.38749457 Simplifying v + -15 = -14.38749457 Reorder the terms: -15 + v = -14.38749457 Solving -15 + v = -14.38749457 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + v = -14.38749457 + 15 Combine like terms: -15 + 15 = 0 0 + v = -14.38749457 + 15 v = -14.38749457 + 15 Combine like terms: -14.38749457 + 15 = 0.61250543 v = 0.61250543 Simplifying v = 0.61250543Solution
The solution to the problem is based on the solutions from the subproblems. v = {29.38749457, 0.61250543}
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