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Simplifying -2v2 + 2v + 15 = 0 Reorder the terms: 15 + 2v + -2v2 = 0 Solving 15 + 2v + -2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -1v + v2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1v + 7.5 + v2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1v + v2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1v + v2 = 0 + 7.5 -1v + v2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1v + v2 = 7.5 The v term is -1v. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1v + 0.25 + v2 = 7.5 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 7.5 + 0.25 Combine like terms: 7.5 + 0.25 = 7.75 0.25 + -1v + v2 = 7.75 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (v + -0.5) equal to 2.783882181 and -2.783882181.Subproblem 1
v + -0.5 = 2.783882181 Simplifying v + -0.5 = 2.783882181 Reorder the terms: -0.5 + v = 2.783882181 Solving -0.5 + v = 2.783882181 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 2.783882181 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 2.783882181 + 0.5 v = 2.783882181 + 0.5 Combine like terms: 2.783882181 + 0.5 = 3.283882181 v = 3.283882181 Simplifying v = 3.283882181Subproblem 2
v + -0.5 = -2.783882181 Simplifying v + -0.5 = -2.783882181 Reorder the terms: -0.5 + v = -2.783882181 Solving -0.5 + v = -2.783882181 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -2.783882181 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -2.783882181 + 0.5 v = -2.783882181 + 0.5 Combine like terms: -2.783882181 + 0.5 = -2.283882181 v = -2.283882181 Simplifying v = -2.283882181Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.283882181, -2.283882181}
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