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Simplifying 15v = v2 + -14 Reorder the terms: 15v = -14 + v2 Solving 15v = -14 + v2 Solving for variable 'v'. Reorder the terms: 14 + 15v + -1v2 = -14 + v2 + 14 + -1v2 Reorder the terms: 14 + 15v + -1v2 = -14 + 14 + v2 + -1v2 Combine like terms: -14 + 14 = 0 14 + 15v + -1v2 = 0 + v2 + -1v2 14 + 15v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 14 + 15v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -15v + v2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -15v + 14 + v2 = 0 + 14 Reorder the terms: -14 + 14 + -15v + v2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -15v + v2 = 0 + 14 -15v + v2 = 0 + 14 Combine like terms: 0 + 14 = 14 -15v + v2 = 14 The v term is -15v. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15v + 56.25 + v2 = 14 + 56.25 Reorder the terms: 56.25 + -15v + v2 = 14 + 56.25 Combine like terms: 14 + 56.25 = 70.25 56.25 + -15v + v2 = 70.25 Factor a perfect square on the left side: (v + -7.5)(v + -7.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (v + -7.5) equal to 8.381527307 and -8.381527307.Subproblem 1
v + -7.5 = 8.381527307 Simplifying v + -7.5 = 8.381527307 Reorder the terms: -7.5 + v = 8.381527307 Solving -7.5 + v = 8.381527307 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + v = 8.381527307 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + v = 8.381527307 + 7.5 v = 8.381527307 + 7.5 Combine like terms: 8.381527307 + 7.5 = 15.881527307 v = 15.881527307 Simplifying v = 15.881527307Subproblem 2
v + -7.5 = -8.381527307 Simplifying v + -7.5 = -8.381527307 Reorder the terms: -7.5 + v = -8.381527307 Solving -7.5 + v = -8.381527307 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + v = -8.381527307 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + v = -8.381527307 + 7.5 v = -8.381527307 + 7.5 Combine like terms: -8.381527307 + 7.5 = -0.881527307 v = -0.881527307 Simplifying v = -0.881527307Solution
The solution to the problem is based on the solutions from the subproblems. v = {15.881527307, -0.881527307}
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