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Simplifying 8v2 + 7v + -23 = 0 Reorder the terms: -23 + 7v + 8v2 = 0 Solving -23 + 7v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.875 + 0.875v + v2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + 0.875v + 2.875 + v2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + 0.875v + v2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + 0.875v + v2 = 0 + 2.875 0.875v + v2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 0.875v + v2 = 2.875 The v term is 0.875v. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875v + 0.19140625 + v2 = 2.875 + 0.19140625 Reorder the terms: 0.19140625 + 0.875v + v2 = 2.875 + 0.19140625 Combine like terms: 2.875 + 0.19140625 = 3.06640625 0.19140625 + 0.875v + v2 = 3.06640625 Factor a perfect square on the left side: (v + 0.4375)(v + 0.4375) = 3.06640625 Calculate the square root of the right side: 1.751115716 Break this problem into two subproblems by setting (v + 0.4375) equal to 1.751115716 and -1.751115716.Subproblem 1
v + 0.4375 = 1.751115716 Simplifying v + 0.4375 = 1.751115716 Reorder the terms: 0.4375 + v = 1.751115716 Solving 0.4375 + v = 1.751115716 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + v = 1.751115716 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + v = 1.751115716 + -0.4375 v = 1.751115716 + -0.4375 Combine like terms: 1.751115716 + -0.4375 = 1.313615716 v = 1.313615716 Simplifying v = 1.313615716Subproblem 2
v + 0.4375 = -1.751115716 Simplifying v + 0.4375 = -1.751115716 Reorder the terms: 0.4375 + v = -1.751115716 Solving 0.4375 + v = -1.751115716 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + v = -1.751115716 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + v = -1.751115716 + -0.4375 v = -1.751115716 + -0.4375 Combine like terms: -1.751115716 + -0.4375 = -2.188615716 v = -2.188615716 Simplifying v = -2.188615716Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.313615716, -2.188615716}
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