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Simplifying 7v2 + -29v + 8 = 0 Reorder the terms: 8 + -29v + 7v2 = 0 Solving 8 + -29v + 7v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + -4.142857143v + v2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -4.142857143v + -1.142857143 + v2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -4.142857143v + v2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -4.142857143v + v2 = 0 + -1.142857143 -4.142857143v + v2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -4.142857143v + v2 = -1.142857143 The v term is -4.142857143v. Take half its coefficient (-2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. -4.142857143v + 4.290816329 + v2 = -1.142857143 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143v + v2 = -1.142857143 + 4.290816329 Combine like terms: -1.142857143 + 4.290816329 = 3.147959186 4.290816329 + -4.142857143v + v2 = 3.147959186 Factor a perfect square on the left side: (v + -2.071428572)(v + -2.071428572) = 3.147959186 Calculate the square root of the right side: 1.774248908 Break this problem into two subproblems by setting (v + -2.071428572) equal to 1.774248908 and -1.774248908.Subproblem 1
v + -2.071428572 = 1.774248908 Simplifying v + -2.071428572 = 1.774248908 Reorder the terms: -2.071428572 + v = 1.774248908 Solving -2.071428572 + v = 1.774248908 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + v = 1.774248908 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + v = 1.774248908 + 2.071428572 v = 1.774248908 + 2.071428572 Combine like terms: 1.774248908 + 2.071428572 = 3.84567748 v = 3.84567748 Simplifying v = 3.84567748Subproblem 2
v + -2.071428572 = -1.774248908 Simplifying v + -2.071428572 = -1.774248908 Reorder the terms: -2.071428572 + v = -1.774248908 Solving -2.071428572 + v = -1.774248908 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + v = -1.774248908 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + v = -1.774248908 + 2.071428572 v = -1.774248908 + 2.071428572 Combine like terms: -1.774248908 + 2.071428572 = 0.297179664 v = 0.297179664 Simplifying v = 0.297179664Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.84567748, 0.297179664}
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