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Simplifying 2v2 + 15v + 18 = v2 + 36 Reorder the terms: 18 + 15v + 2v2 = v2 + 36 Reorder the terms: 18 + 15v + 2v2 = 36 + v2 Solving 18 + 15v + 2v2 = 36 + v2 Solving for variable 'v'. Reorder the terms: 18 + -36 + 15v + 2v2 + -1v2 = 36 + v2 + -36 + -1v2 Combine like terms: 18 + -36 = -18 -18 + 15v + 2v2 + -1v2 = 36 + v2 + -36 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 -18 + 15v + 1v2 = 36 + v2 + -36 + -1v2 Reorder the terms: -18 + 15v + 1v2 = 36 + -36 + v2 + -1v2 Combine like terms: 36 + -36 = 0 -18 + 15v + 1v2 = 0 + v2 + -1v2 -18 + 15v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -18 + 15v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 15v + 18 + v2 = 0 + 18 Reorder the terms: -18 + 18 + 15v + v2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 15v + v2 = 0 + 18 15v + v2 = 0 + 18 Combine like terms: 0 + 18 = 18 15v + v2 = 18 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 = 18 + 56.25 Reorder the terms: 56.25 + 15v + v2 = 18 + 56.25 Combine like terms: 18 + 56.25 = 74.25 56.25 + 15v + v2 = 74.25 Factor a perfect square on the left side: (v + 7.5)(v + 7.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (v + 7.5) equal to 8.61684397 and -8.61684397.Subproblem 1
v + 7.5 = 8.61684397 Simplifying v + 7.5 = 8.61684397 Reorder the terms: 7.5 + v = 8.61684397 Solving 7.5 + v = 8.61684397 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 = 8.61684397 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = 8.61684397 + -7.5 v = 8.61684397 + -7.5 Combine like terms: 8.61684397 + -7.5 = 1.11684397 v = 1.11684397 Simplifying v = 1.11684397Subproblem 2
v + 7.5 = -8.61684397 Simplifying v + 7.5 = -8.61684397 Reorder the terms: 7.5 + v = -8.61684397 Solving 7.5 + v = -8.61684397 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 = -8.61684397 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = -8.61684397 + -7.5 v = -8.61684397 + -7.5 Combine like terms: -8.61684397 + -7.5 = -16.11684397 v = -16.11684397 Simplifying v = -16.11684397Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.11684397, -16.11684397}
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