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Simplifying 315 = 0.03v2 + v Reorder the terms: 315 = v + 0.03v2 Solving 315 = v + 0.03v2 Solving for variable 'v'. Reorder the terms: 315 + -1v + -0.03v2 = v + -1v + 0.03v2 + -0.03v2 Combine like terms: v + -1v = 0 315 + -1v + -0.03v2 = 0 + 0.03v2 + -0.03v2 315 + -1v + -0.03v2 = 0.03v2 + -0.03v2 Combine like terms: 0.03v2 + -0.03v2 = 0.00 315 + -1v + -0.03v2 = 0.00 Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. -10500 + 33.33333333v + v2 = 0 Move the constant term to the right: Add '10500' to each side of the equation. -10500 + 33.33333333v + 10500 + v2 = 0 + 10500 Reorder the terms: -10500 + 10500 + 33.33333333v + v2 = 0 + 10500 Combine like terms: -10500 + 10500 = 0 0 + 33.33333333v + v2 = 0 + 10500 33.33333333v + v2 = 0 + 10500 Combine like terms: 0 + 10500 = 10500 33.33333333v + v2 = 10500 The v term is 33.33333333v. Take half its coefficient (16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. 33.33333333v + 277.7777779 + v2 = 10500 + 277.7777779 Reorder the terms: 277.7777779 + 33.33333333v + v2 = 10500 + 277.7777779 Combine like terms: 10500 + 277.7777779 = 10777.7777779 277.7777779 + 33.33333333v + v2 = 10777.7777779 Factor a perfect square on the left side: (v + 16.66666667)(v + 16.66666667) = 10777.7777779 Calculate the square root of the right side: 103.816076683 Break this problem into two subproblems by setting (v + 16.66666667) equal to 103.816076683 and -103.816076683.Subproblem 1
v + 16.66666667 = 103.816076683 Simplifying v + 16.66666667 = 103.816076683 Reorder the terms: 16.66666667 + v = 103.816076683 Solving 16.66666667 + v = 103.816076683 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + v = 103.816076683 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + v = 103.816076683 + -16.66666667 v = 103.816076683 + -16.66666667 Combine like terms: 103.816076683 + -16.66666667 = 87.149410013 v = 87.149410013 Simplifying v = 87.149410013Subproblem 2
v + 16.66666667 = -103.816076683 Simplifying v + 16.66666667 = -103.816076683 Reorder the terms: 16.66666667 + v = -103.816076683 Solving 16.66666667 + v = -103.816076683 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + v = -103.816076683 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + v = -103.816076683 + -16.66666667 v = -103.816076683 + -16.66666667 Combine like terms: -103.816076683 + -16.66666667 = -120.482743353 v = -120.482743353 Simplifying v = -120.482743353Solution
The solution to the problem is based on the solutions from the subproblems. v = {87.149410013, -120.482743353}
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