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Simplifying 50 = 0.006v2 + 0.3v Reorder the terms: 50 = 0.3v + 0.006v2 Solving 50 = 0.3v + 0.006v2 Solving for variable 'v'. Reorder the terms: 50 + -0.3v + -0.006v2 = 0.3v + -0.3v + 0.006v2 + -0.006v2 Combine like terms: 0.3v + -0.3v = 0.0 50 + -0.3v + -0.006v2 = 0.0 + 0.006v2 + -0.006v2 50 + -0.3v + -0.006v2 = 0.006v2 + -0.006v2 Combine like terms: 0.006v2 + -0.006v2 = 0.000 50 + -0.3v + -0.006v2 = 0.000 Begin completing the square. Divide all terms by -0.006 the coefficient of the squared term: Divide each side by '-0.006'. -8333.333333 + 50v + v2 = 0 Move the constant term to the right: Add '8333.333333' to each side of the equation. -8333.333333 + 50v + 8333.333333 + v2 = 0 + 8333.333333 Reorder the terms: -8333.333333 + 8333.333333 + 50v + v2 = 0 + 8333.333333 Combine like terms: -8333.333333 + 8333.333333 = 0.000000 0.000000 + 50v + v2 = 0 + 8333.333333 50v + v2 = 0 + 8333.333333 Combine like terms: 0 + 8333.333333 = 8333.333333 50v + v2 = 8333.333333 The v term is 50v. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50v + 625 + v2 = 8333.333333 + 625 Reorder the terms: 625 + 50v + v2 = 8333.333333 + 625 Combine like terms: 8333.333333 + 625 = 8958.333333 625 + 50v + v2 = 8958.333333 Factor a perfect square on the left side: (v + 25)(v + 25) = 8958.333333 Calculate the square root of the right side: 94.648472428 Break this problem into two subproblems by setting (v + 25) equal to 94.648472428 and -94.648472428.Subproblem 1
v + 25 = 94.648472428 Simplifying v + 25 = 94.648472428 Reorder the terms: 25 + v = 94.648472428 Solving 25 + v = 94.648472428 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + v = 94.648472428 + -25 Combine like terms: 25 + -25 = 0 0 + v = 94.648472428 + -25 v = 94.648472428 + -25 Combine like terms: 94.648472428 + -25 = 69.648472428 v = 69.648472428 Simplifying v = 69.648472428Subproblem 2
v + 25 = -94.648472428 Simplifying v + 25 = -94.648472428 Reorder the terms: 25 + v = -94.648472428 Solving 25 + v = -94.648472428 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + v = -94.648472428 + -25 Combine like terms: 25 + -25 = 0 0 + v = -94.648472428 + -25 v = -94.648472428 + -25 Combine like terms: -94.648472428 + -25 = -119.648472428 v = -119.648472428 Simplifying v = -119.648472428Solution
The solution to the problem is based on the solutions from the subproblems. v = {69.648472428, -119.648472428}
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