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Simplifying 0 = v2 + -15v + 2 Reorder the terms: 0 = 2 + -15v + v2 Solving 0 = 2 + -15v + v2 Solving for variable 'v'. Combine like terms: 0 + -2 = -2 -2 + 15v + -1v2 = 2 + -15v + v2 + -2 + 15v + -1v2 Reorder the terms: -2 + 15v + -1v2 = 2 + -2 + -15v + 15v + v2 + -1v2 Combine like terms: 2 + -2 = 0 -2 + 15v + -1v2 = 0 + -15v + 15v + v2 + -1v2 -2 + 15v + -1v2 = -15v + 15v + v2 + -1v2 Combine like terms: -15v + 15v = 0 -2 + 15v + -1v2 = 0 + v2 + -1v2 -2 + 15v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -2 + 15v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -15v + v2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -15v + -2 + v2 = 0 + -2 Reorder the terms: 2 + -2 + -15v + v2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -15v + v2 = 0 + -2 -15v + v2 = 0 + -2 Combine like terms: 0 + -2 = -2 -15v + v2 = -2 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 = -2 + 56.25 Reorder the terms: 56.25 + -15v + v2 = -2 + 56.25 Combine like terms: -2 + 56.25 = 54.25 56.25 + -15v + v2 = 54.25 Factor a perfect square on the left side: (v + -7.5)(v + -7.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (v + -7.5) equal to 7.365459931 and -7.365459931.Subproblem 1
v + -7.5 = 7.365459931 Simplifying v + -7.5 = 7.365459931 Reorder the terms: -7.5 + v = 7.365459931 Solving -7.5 + v = 7.365459931 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 = 7.365459931 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + v = 7.365459931 + 7.5 v = 7.365459931 + 7.5 Combine like terms: 7.365459931 + 7.5 = 14.865459931 v = 14.865459931 Simplifying v = 14.865459931Subproblem 2
v + -7.5 = -7.365459931 Simplifying v + -7.5 = -7.365459931 Reorder the terms: -7.5 + v = -7.365459931 Solving -7.5 + v = -7.365459931 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 = -7.365459931 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + v = -7.365459931 + 7.5 v = -7.365459931 + 7.5 Combine like terms: -7.365459931 + 7.5 = 0.134540069 v = 0.134540069 Simplifying v = 0.134540069Solution
The solution to the problem is based on the solutions from the subproblems. v = {14.865459931, 0.134540069}
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