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Simplifying 7v2 + -7v + -3 = 0 Reorder the terms: -3 + -7v + 7v2 = 0 Solving -3 + -7v + 7v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -1v + v2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1v + 0.4285714286 + v2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1v + v2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1v + v2 = 0 + 0.4285714286 -1v + v2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1v + v2 = 0.4285714286 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 = 0.4285714286 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 0.4285714286 + 0.25 Combine like terms: 0.4285714286 + 0.25 = 0.6785714286 0.25 + -1v + v2 = 0.6785714286 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 0.6785714286 Calculate the square root of the right side: 0.823754471 Break this problem into two subproblems by setting (v + -0.5) equal to 0.823754471 and -0.823754471.Subproblem 1
v + -0.5 = 0.823754471 Simplifying v + -0.5 = 0.823754471 Reorder the terms: -0.5 + v = 0.823754471 Solving -0.5 + v = 0.823754471 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 = 0.823754471 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 0.823754471 + 0.5 v = 0.823754471 + 0.5 Combine like terms: 0.823754471 + 0.5 = 1.323754471 v = 1.323754471 Simplifying v = 1.323754471Subproblem 2
v + -0.5 = -0.823754471 Simplifying v + -0.5 = -0.823754471 Reorder the terms: -0.5 + v = -0.823754471 Solving -0.5 + v = -0.823754471 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 = -0.823754471 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -0.823754471 + 0.5 v = -0.823754471 + 0.5 Combine like terms: -0.823754471 + 0.5 = -0.323754471 v = -0.323754471 Simplifying v = -0.323754471Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.323754471, -0.323754471}
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