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Simplifying (v + -7)(v + -2) = 2 Reorder the terms: (-7 + v)(v + -2) = 2 Reorder the terms: (-7 + v)(-2 + v) = 2 Multiply (-7 + v) * (-2 + v) (-7(-2 + v) + v(-2 + v)) = 2 ((-2 * -7 + v * -7) + v(-2 + v)) = 2 ((14 + -7v) + v(-2 + v)) = 2 (14 + -7v + (-2 * v + v * v)) = 2 (14 + -7v + (-2v + v2)) = 2 Combine like terms: -7v + -2v = -9v (14 + -9v + v2) = 2 Solving 14 + -9v + v2 = 2 Solving for variable 'v'. Reorder the terms: 14 + -2 + -9v + v2 = 2 + -2 Combine like terms: 14 + -2 = 12 12 + -9v + v2 = 2 + -2 Combine like terms: 2 + -2 = 0 12 + -9v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -9v + -12 + v2 = 0 + -12 Reorder the terms: 12 + -12 + -9v + v2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -9v + v2 = 0 + -12 -9v + v2 = 0 + -12 Combine like terms: 0 + -12 = -12 -9v + v2 = -12 The v term is -9v. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9v + 20.25 + v2 = -12 + 20.25 Reorder the terms: 20.25 + -9v + v2 = -12 + 20.25 Combine like terms: -12 + 20.25 = 8.25 20.25 + -9v + v2 = 8.25 Factor a perfect square on the left side: (v + -4.5)(v + -4.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (v + -4.5) equal to 2.872281323 and -2.872281323.Subproblem 1
v + -4.5 = 2.872281323 Simplifying v + -4.5 = 2.872281323 Reorder the terms: -4.5 + v = 2.872281323 Solving -4.5 + v = 2.872281323 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = 2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = 2.872281323 + 4.5 v = 2.872281323 + 4.5 Combine like terms: 2.872281323 + 4.5 = 7.372281323 v = 7.372281323 Simplifying v = 7.372281323Subproblem 2
v + -4.5 = -2.872281323 Simplifying v + -4.5 = -2.872281323 Reorder the terms: -4.5 + v = -2.872281323 Solving -4.5 + v = -2.872281323 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = -2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = -2.872281323 + 4.5 v = -2.872281323 + 4.5 Combine like terms: -2.872281323 + 4.5 = 1.627718677 v = 1.627718677 Simplifying v = 1.627718677Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.372281323, 1.627718677}
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