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Simplifying (8v2 + 8v) + -1(-2v2 + -8v + 3) = 0 Reorder the terms: (8v + 8v2) + -1(-2v2 + -8v + 3) = 0 Remove parenthesis around (8v + 8v2) 8v + 8v2 + -1(-2v2 + -8v + 3) = 0 Reorder the terms: 8v + 8v2 + -1(3 + -8v + -2v2) = 0 8v + 8v2 + (3 * -1 + -8v * -1 + -2v2 * -1) = 0 8v + 8v2 + (-3 + 8v + 2v2) = 0 Reorder the terms: -3 + 8v + 8v + 8v2 + 2v2 = 0 Combine like terms: 8v + 8v = 16v -3 + 16v + 8v2 + 2v2 = 0 Combine like terms: 8v2 + 2v2 = 10v2 -3 + 16v + 10v2 = 0 Solving -3 + 16v + 10v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 1.6v + v2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 1.6v + 0.3 + v2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 1.6v + v2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 1.6v + v2 = 0.0 + 0.3 1.6v + v2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 1.6v + v2 = 0.3 The v term is 1.6v. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6v + 0.64 + v2 = 0.3 + 0.64 Reorder the terms: 0.64 + 1.6v + v2 = 0.3 + 0.64 Combine like terms: 0.3 + 0.64 = 0.94 0.64 + 1.6v + v2 = 0.94 Factor a perfect square on the left side: (v + 0.8)(v + 0.8) = 0.94 Calculate the square root of the right side: 0.969535971 Break this problem into two subproblems by setting (v + 0.8) equal to 0.969535971 and -0.969535971.Subproblem 1
v + 0.8 = 0.969535971 Simplifying v + 0.8 = 0.969535971 Reorder the terms: 0.8 + v = 0.969535971 Solving 0.8 + v = 0.969535971 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + v = 0.969535971 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = 0.969535971 + -0.8 v = 0.969535971 + -0.8 Combine like terms: 0.969535971 + -0.8 = 0.169535971 v = 0.169535971 Simplifying v = 0.169535971Subproblem 2
v + 0.8 = -0.969535971 Simplifying v + 0.8 = -0.969535971 Reorder the terms: 0.8 + v = -0.969535971 Solving 0.8 + v = -0.969535971 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + v = -0.969535971 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = -0.969535971 + -0.8 v = -0.969535971 + -0.8 Combine like terms: -0.969535971 + -0.8 = -1.769535971 v = -1.769535971 Simplifying v = -1.769535971Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.169535971, -1.769535971}
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