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Simplifying (4v2 + -12v + 8) + -1(v + 1)(3) = -3 Reorder the terms: (8 + -12v + 4v2) + -1(v + 1)(3) = -3 Remove parenthesis around (8 + -12v + 4v2) 8 + -12v + 4v2 + -1(v + 1)(3) = -3 Reorder the terms: 8 + -12v + 4v2 + -1(1 + v)(3) = -3 Reorder the terms for easier multiplication: 8 + -12v + 4v2 + -1 * 3(1 + v) = -3 Multiply -1 * 3 8 + -12v + 4v2 + -3(1 + v) = -3 8 + -12v + 4v2 + (1 * -3 + v * -3) = -3 8 + -12v + 4v2 + (-3 + -3v) = -3 Reorder the terms: 8 + -3 + -12v + -3v + 4v2 = -3 Combine like terms: 8 + -3 = 5 5 + -12v + -3v + 4v2 = -3 Combine like terms: -12v + -3v = -15v 5 + -15v + 4v2 = -3 Solving 5 + -15v + 4v2 = -3 Solving for variable 'v'. Reorder the terms: 5 + 3 + -15v + 4v2 = -3 + 3 Combine like terms: 5 + 3 = 8 8 + -15v + 4v2 = -3 + 3 Combine like terms: -3 + 3 = 0 8 + -15v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + -3.75v + v2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.75v + -2 + v2 = 0 + -2 Reorder the terms: 2 + -2 + -3.75v + v2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.75v + v2 = 0 + -2 -3.75v + v2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.75v + v2 = -2 The v term is -3.75v. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75v + 3.515625 + v2 = -2 + 3.515625 Reorder the terms: 3.515625 + -3.75v + v2 = -2 + 3.515625 Combine like terms: -2 + 3.515625 = 1.515625 3.515625 + -3.75v + v2 = 1.515625 Factor a perfect square on the left side: (v + -1.875)(v + -1.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (v + -1.875) equal to 1.231107225 and -1.231107225.Subproblem 1
v + -1.875 = 1.231107225 Simplifying v + -1.875 = 1.231107225 Reorder the terms: -1.875 + v = 1.231107225 Solving -1.875 + v = 1.231107225 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + v = 1.231107225 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + v = 1.231107225 + 1.875 v = 1.231107225 + 1.875 Combine like terms: 1.231107225 + 1.875 = 3.106107225 v = 3.106107225 Simplifying v = 3.106107225Subproblem 2
v + -1.875 = -1.231107225 Simplifying v + -1.875 = -1.231107225 Reorder the terms: -1.875 + v = -1.231107225 Solving -1.875 + v = -1.231107225 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + v = -1.231107225 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + v = -1.231107225 + 1.875 v = -1.231107225 + 1.875 Combine like terms: -1.231107225 + 1.875 = 0.643892775 v = 0.643892775 Simplifying v = 0.643892775Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.106107225, 0.643892775}
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