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Simplifying 5v2 + -9v + -5 = 0 Reorder the terms: -5 + -9v + 5v2 = 0 Solving -5 + -9v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -1.8v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.8v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -1.8v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.8v + v2 = 0 + 1 -1.8v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.8v + v2 = 1 The v term is -1.8v. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8v + 0.81 + v2 = 1 + 0.81 Reorder the terms: 0.81 + -1.8v + v2 = 1 + 0.81 Combine like terms: 1 + 0.81 = 1.81 0.81 + -1.8v + v2 = 1.81 Factor a perfect square on the left side: (v + -0.9)(v + -0.9) = 1.81 Calculate the square root of the right side: 1.345362405 Break this problem into two subproblems by setting (v + -0.9) equal to 1.345362405 and -1.345362405.Subproblem 1
v + -0.9 = 1.345362405 Simplifying v + -0.9 = 1.345362405 Reorder the terms: -0.9 + v = 1.345362405 Solving -0.9 + v = 1.345362405 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + v = 1.345362405 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + v = 1.345362405 + 0.9 v = 1.345362405 + 0.9 Combine like terms: 1.345362405 + 0.9 = 2.245362405 v = 2.245362405 Simplifying v = 2.245362405Subproblem 2
v + -0.9 = -1.345362405 Simplifying v + -0.9 = -1.345362405 Reorder the terms: -0.9 + v = -1.345362405 Solving -0.9 + v = -1.345362405 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + v = -1.345362405 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + v = -1.345362405 + 0.9 v = -1.345362405 + 0.9 Combine like terms: -1.345362405 + 0.9 = -0.445362405 v = -0.445362405 Simplifying v = -0.445362405Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.245362405, -0.445362405}
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