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Simplifying 8v2 + -2v = 19 Reorder the terms: -2v + 8v2 = 19 Solving -2v + 8v2 = 19 Solving for variable 'v'. Reorder the terms: -19 + -2v + 8v2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -2v + 8v2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.375 + -0.25v + v2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -0.25v + 2.375 + v2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -0.25v + v2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -0.25v + v2 = 0 + 2.375 -0.25v + v2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -0.25v + v2 = 2.375 The v term is -0.25v. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25v + 0.015625 + v2 = 2.375 + 0.015625 Reorder the terms: 0.015625 + -0.25v + v2 = 2.375 + 0.015625 Combine like terms: 2.375 + 0.015625 = 2.390625 0.015625 + -0.25v + v2 = 2.390625 Factor a perfect square on the left side: (v + -0.125)(v + -0.125) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (v + -0.125) equal to 1.54616461 and -1.54616461.Subproblem 1
v + -0.125 = 1.54616461 Simplifying v + -0.125 = 1.54616461 Reorder the terms: -0.125 + v = 1.54616461 Solving -0.125 + v = 1.54616461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + v = 1.54616461 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + v = 1.54616461 + 0.125 v = 1.54616461 + 0.125 Combine like terms: 1.54616461 + 0.125 = 1.67116461 v = 1.67116461 Simplifying v = 1.67116461Subproblem 2
v + -0.125 = -1.54616461 Simplifying v + -0.125 = -1.54616461 Reorder the terms: -0.125 + v = -1.54616461 Solving -0.125 + v = -1.54616461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + v = -1.54616461 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + v = -1.54616461 + 0.125 v = -1.54616461 + 0.125 Combine like terms: -1.54616461 + 0.125 = -1.42116461 v = -1.42116461 Simplifying v = -1.42116461Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.67116461, -1.42116461}
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