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Simplifying -6v2 + 8v + 3 = 0 Reorder the terms: 3 + 8v + -6v2 = 0 Solving 3 + 8v + -6v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.5 + -1.333333333v + v2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.333333333v + 0.5 + v2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.333333333v + v2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.333333333v + v2 = 0 + 0.5 -1.333333333v + v2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.333333333v + v2 = 0.5 The v term is -1.333333333v. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333v + 0.4444444442 + v2 = 0.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333v + v2 = 0.5 + 0.4444444442 Combine like terms: 0.5 + 0.4444444442 = 0.9444444442 0.4444444442 + -1.333333333v + v2 = 0.9444444442 Factor a perfect square on the left side: (v + -0.6666666665)(v + -0.6666666665) = 0.9444444442 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (v + -0.6666666665) equal to 0.971825316 and -0.971825316.Subproblem 1
v + -0.6666666665 = 0.971825316 Simplifying v + -0.6666666665 = 0.971825316 Reorder the terms: -0.6666666665 + v = 0.971825316 Solving -0.6666666665 + v = 0.971825316 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + v = 0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + v = 0.971825316 + 0.6666666665 v = 0.971825316 + 0.6666666665 Combine like terms: 0.971825316 + 0.6666666665 = 1.6384919825 v = 1.6384919825 Simplifying v = 1.6384919825Subproblem 2
v + -0.6666666665 = -0.971825316 Simplifying v + -0.6666666665 = -0.971825316 Reorder the terms: -0.6666666665 + v = -0.971825316 Solving -0.6666666665 + v = -0.971825316 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + v = -0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + v = -0.971825316 + 0.6666666665 v = -0.971825316 + 0.6666666665 Combine like terms: -0.971825316 + 0.6666666665 = -0.3051586495 v = -0.3051586495 Simplifying v = -0.3051586495Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.6384919825, -0.3051586495}
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