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Simplifying 2v2 + 16v + 15 = v2 + 36 Reorder the terms: 15 + 16v + 2v2 = v2 + 36 Reorder the terms: 15 + 16v + 2v2 = 36 + v2 Solving 15 + 16v + 2v2 = 36 + v2 Solving for variable 'v'. Reorder the terms: 15 + -36 + 16v + 2v2 + -1v2 = 36 + v2 + -36 + -1v2 Combine like terms: 15 + -36 = -21 -21 + 16v + 2v2 + -1v2 = 36 + v2 + -36 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 -21 + 16v + 1v2 = 36 + v2 + -36 + -1v2 Reorder the terms: -21 + 16v + 1v2 = 36 + -36 + v2 + -1v2 Combine like terms: 36 + -36 = 0 -21 + 16v + 1v2 = 0 + v2 + -1v2 -21 + 16v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -21 + 16v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 16v + 21 + v2 = 0 + 21 Reorder the terms: -21 + 21 + 16v + v2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 16v + v2 = 0 + 21 16v + v2 = 0 + 21 Combine like terms: 0 + 21 = 21 16v + v2 = 21 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 = 21 + 64 Reorder the terms: 64 + 16v + v2 = 21 + 64 Combine like terms: 21 + 64 = 85 64 + 16v + v2 = 85 Factor a perfect square on the left side: (v + 8)(v + 8) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (v + 8) equal to 9.219544457 and -9.219544457.Subproblem 1
v + 8 = 9.219544457 Simplifying v + 8 = 9.219544457 Reorder the terms: 8 + v = 9.219544457 Solving 8 + v = 9.219544457 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 = 9.219544457 + -8 Combine like terms: 8 + -8 = 0 0 + v = 9.219544457 + -8 v = 9.219544457 + -8 Combine like terms: 9.219544457 + -8 = 1.219544457 v = 1.219544457 Simplifying v = 1.219544457Subproblem 2
v + 8 = -9.219544457 Simplifying v + 8 = -9.219544457 Reorder the terms: 8 + v = -9.219544457 Solving 8 + v = -9.219544457 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 = -9.219544457 + -8 Combine like terms: 8 + -8 = 0 0 + v = -9.219544457 + -8 v = -9.219544457 + -8 Combine like terms: -9.219544457 + -8 = -17.219544457 v = -17.219544457 Simplifying v = -17.219544457Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.219544457, -17.219544457}
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