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Simplifying 8v2 + -8v + -13 = 0 Reorder the terms: -13 + -8v + 8v2 = 0 Solving -13 + -8v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -1v + v2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -1v + 1.625 + v2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -1v + v2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -1v + v2 = 0 + 1.625 -1v + v2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -1v + v2 = 1.625 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 = 1.625 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 1.625 + 0.25 Combine like terms: 1.625 + 0.25 = 1.875 0.25 + -1v + v2 = 1.875 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 1.875 Calculate the square root of the right side: 1.369306394 Break this problem into two subproblems by setting (v + -0.5) equal to 1.369306394 and -1.369306394.Subproblem 1
v + -0.5 = 1.369306394 Simplifying v + -0.5 = 1.369306394 Reorder the terms: -0.5 + v = 1.369306394 Solving -0.5 + v = 1.369306394 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 = 1.369306394 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 1.369306394 + 0.5 v = 1.369306394 + 0.5 Combine like terms: 1.369306394 + 0.5 = 1.869306394 v = 1.869306394 Simplifying v = 1.869306394Subproblem 2
v + -0.5 = -1.369306394 Simplifying v + -0.5 = -1.369306394 Reorder the terms: -0.5 + v = -1.369306394 Solving -0.5 + v = -1.369306394 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 = -1.369306394 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -1.369306394 + 0.5 v = -1.369306394 + 0.5 Combine like terms: -1.369306394 + 0.5 = -0.869306394 v = -0.869306394 Simplifying v = -0.869306394Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.869306394, -0.869306394}
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