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Simplifying 70 = 0.04v2 + -0.5v Reorder the terms: 70 = -0.5v + 0.04v2 Solving 70 = -0.5v + 0.04v2 Solving for variable 'v'. Reorder the terms: 70 + 0.5v + -0.04v2 = -0.5v + 0.5v + 0.04v2 + -0.04v2 Combine like terms: -0.5v + 0.5v = 0.0 70 + 0.5v + -0.04v2 = 0.0 + 0.04v2 + -0.04v2 70 + 0.5v + -0.04v2 = 0.04v2 + -0.04v2 Combine like terms: 0.04v2 + -0.04v2 = 0.00 70 + 0.5v + -0.04v2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -1750 + -12.5v + v2 = 0 Move the constant term to the right: Add '1750' to each side of the equation. -1750 + -12.5v + 1750 + v2 = 0 + 1750 Reorder the terms: -1750 + 1750 + -12.5v + v2 = 0 + 1750 Combine like terms: -1750 + 1750 = 0 0 + -12.5v + v2 = 0 + 1750 -12.5v + v2 = 0 + 1750 Combine like terms: 0 + 1750 = 1750 -12.5v + v2 = 1750 The v term is -12.5v. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5v + 39.0625 + v2 = 1750 + 39.0625 Reorder the terms: 39.0625 + -12.5v + v2 = 1750 + 39.0625 Combine like terms: 1750 + 39.0625 = 1789.0625 39.0625 + -12.5v + v2 = 1789.0625 Factor a perfect square on the left side: (v + -6.25)(v + -6.25) = 1789.0625 Calculate the square root of the right side: 42.297310789 Break this problem into two subproblems by setting (v + -6.25) equal to 42.297310789 and -42.297310789.Subproblem 1
v + -6.25 = 42.297310789 Simplifying v + -6.25 = 42.297310789 Reorder the terms: -6.25 + v = 42.297310789 Solving -6.25 + v = 42.297310789 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + v = 42.297310789 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + v = 42.297310789 + 6.25 v = 42.297310789 + 6.25 Combine like terms: 42.297310789 + 6.25 = 48.547310789 v = 48.547310789 Simplifying v = 48.547310789Subproblem 2
v + -6.25 = -42.297310789 Simplifying v + -6.25 = -42.297310789 Reorder the terms: -6.25 + v = -42.297310789 Solving -6.25 + v = -42.297310789 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + v = -42.297310789 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + v = -42.297310789 + 6.25 v = -42.297310789 + 6.25 Combine like terms: -42.297310789 + 6.25 = -36.047310789 v = -36.047310789 Simplifying v = -36.047310789Solution
The solution to the problem is based on the solutions from the subproblems. v = {48.547310789, -36.047310789}
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