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Simplifying 0.0066 = 0.00113v + 0.0000044v2 Solving 0.0066 = 0.00113v + 0.0000044v2 Solving for variable 'v'. Reorder the terms: 0.0066 + -0.00113v + -0.0000044v2 = 0.00113v + -0.00113v + 0.0000044v2 + -0.0000044v2 Combine like terms: 0.00113v + -0.00113v = 0.00000 0.0066 + -0.00113v + -0.0000044v2 = 0.00000 + 0.0000044v2 + -0.0000044v2 0.0066 + -0.00113v + -0.0000044v2 = 0.0000044v2 + -0.0000044v2 Combine like terms: 0.0000044v2 + -0.0000044v2 = 0.0000000 0.0066 + -0.00113v + -0.0000044v2 = 0.0000000 Begin completing the square. Divide all terms by -0.0000044 the coefficient of the squared term: Divide each side by '-0.0000044'. -1500 + 256.8181818v + v2 = 0 Move the constant term to the right: Add '1500' to each side of the equation. -1500 + 256.8181818v + 1500 + v2 = 0 + 1500 Reorder the terms: -1500 + 1500 + 256.8181818v + v2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + 256.8181818v + v2 = 0 + 1500 256.8181818v + v2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 256.8181818v + v2 = 1500 The v term is 256.8181818v. Take half its coefficient (128.4090909). Square it (16488.89463) and add it to both sides. Add '16488.89463' to each side of the equation. 256.8181818v + 16488.89463 + v2 = 1500 + 16488.89463 Reorder the terms: 16488.89463 + 256.8181818v + v2 = 1500 + 16488.89463 Combine like terms: 1500 + 16488.89463 = 17988.89463 16488.89463 + 256.8181818v + v2 = 17988.89463 Factor a perfect square on the left side: (v + 128.4090909)(v + 128.4090909) = 17988.89463 Calculate the square root of the right side: 134.122684994 Break this problem into two subproblems by setting (v + 128.4090909) equal to 134.122684994 and -134.122684994.Subproblem 1
v + 128.4090909 = 134.122684994 Simplifying v + 128.4090909 = 134.122684994 Reorder the terms: 128.4090909 + v = 134.122684994 Solving 128.4090909 + v = 134.122684994 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-128.4090909' to each side of the equation. 128.4090909 + -128.4090909 + v = 134.122684994 + -128.4090909 Combine like terms: 128.4090909 + -128.4090909 = 0.0000000 0.0000000 + v = 134.122684994 + -128.4090909 v = 134.122684994 + -128.4090909 Combine like terms: 134.122684994 + -128.4090909 = 5.713594094 v = 5.713594094 Simplifying v = 5.713594094Subproblem 2
v + 128.4090909 = -134.122684994 Simplifying v + 128.4090909 = -134.122684994 Reorder the terms: 128.4090909 + v = -134.122684994 Solving 128.4090909 + v = -134.122684994 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-128.4090909' to each side of the equation. 128.4090909 + -128.4090909 + v = -134.122684994 + -128.4090909 Combine like terms: 128.4090909 + -128.4090909 = 0.0000000 0.0000000 + v = -134.122684994 + -128.4090909 v = -134.122684994 + -128.4090909 Combine like terms: -134.122684994 + -128.4090909 = -262.531775894 v = -262.531775894 Simplifying v = -262.531775894Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.713594094, -262.531775894}
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