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Simplifying 1.5(0.28) * v + 0.06v2 = 129 Multiply 1.5 * 0.28 0.42v + 0.06v2 = 129 Solving 0.42v + 0.06v2 = 129 Solving for variable 'v'. Reorder the terms: -129 + 0.42v + 0.06v2 = 129 + -129 Combine like terms: 129 + -129 = 0 -129 + 0.42v + 0.06v2 = 0 Begin completing the square. Divide all terms by 0.06 the coefficient of the squared term: Divide each side by '0.06'. -2150 + 7v + v2 = 0 Move the constant term to the right: Add '2150' to each side of the equation. -2150 + 7v + 2150 + v2 = 0 + 2150 Reorder the terms: -2150 + 2150 + 7v + v2 = 0 + 2150 Combine like terms: -2150 + 2150 = 0 0 + 7v + v2 = 0 + 2150 7v + v2 = 0 + 2150 Combine like terms: 0 + 2150 = 2150 7v + v2 = 2150 The v term is 7v. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7v + 12.25 + v2 = 2150 + 12.25 Reorder the terms: 12.25 + 7v + v2 = 2150 + 12.25 Combine like terms: 2150 + 12.25 = 2162.25 12.25 + 7v + v2 = 2162.25 Factor a perfect square on the left side: (v + 3.5)(v + 3.5) = 2162.25 Calculate the square root of the right side: 46.5 Break this problem into two subproblems by setting (v + 3.5) equal to 46.5 and -46.5.Subproblem 1
v + 3.5 = 46.5 Simplifying v + 3.5 = 46.5 Reorder the terms: 3.5 + v = 46.5 Solving 3.5 + v = 46.5 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = 46.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = 46.5 + -3.5 v = 46.5 + -3.5 Combine like terms: 46.5 + -3.5 = 43 v = 43 Simplifying v = 43Subproblem 2
v + 3.5 = -46.5 Simplifying v + 3.5 = -46.5 Reorder the terms: 3.5 + v = -46.5 Solving 3.5 + v = -46.5 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = -46.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = -46.5 + -3.5 v = -46.5 + -3.5 Combine like terms: -46.5 + -3.5 = -50 v = -50 Simplifying v = -50Solution
The solution to the problem is based on the solutions from the subproblems. v = {43, -50}
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