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Simplifying (5v2 + -8v + -8) + -1(8v2 + 3v + -6) + (5v2 + -3v + 1) = 0 Reorder the terms: (-8 + -8v + 5v2) + -1(8v2 + 3v + -6) + (5v2 + -3v + 1) = 0 Remove parenthesis around (-8 + -8v + 5v2) -8 + -8v + 5v2 + -1(8v2 + 3v + -6) + (5v2 + -3v + 1) = 0 Reorder the terms: -8 + -8v + 5v2 + -1(-6 + 3v + 8v2) + (5v2 + -3v + 1) = 0 -8 + -8v + 5v2 + (-6 * -1 + 3v * -1 + 8v2 * -1) + (5v2 + -3v + 1) = 0 -8 + -8v + 5v2 + (6 + -3v + -8v2) + (5v2 + -3v + 1) = 0 Reorder the terms: -8 + -8v + 5v2 + 6 + -3v + -8v2 + (1 + -3v + 5v2) = 0 Remove parenthesis around (1 + -3v + 5v2) -8 + -8v + 5v2 + 6 + -3v + -8v2 + 1 + -3v + 5v2 = 0 Reorder the terms: -8 + 6 + 1 + -8v + -3v + -3v + 5v2 + -8v2 + 5v2 = 0 Combine like terms: -8 + 6 = -2 -2 + 1 + -8v + -3v + -3v + 5v2 + -8v2 + 5v2 = 0 Combine like terms: -2 + 1 = -1 -1 + -8v + -3v + -3v + 5v2 + -8v2 + 5v2 = 0 Combine like terms: -8v + -3v = -11v -1 + -11v + -3v + 5v2 + -8v2 + 5v2 = 0 Combine like terms: -11v + -3v = -14v -1 + -14v + 5v2 + -8v2 + 5v2 = 0 Combine like terms: 5v2 + -8v2 = -3v2 -1 + -14v + -3v2 + 5v2 = 0 Combine like terms: -3v2 + 5v2 = 2v2 -1 + -14v + 2v2 = 0 Solving -1 + -14v + 2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -7v + v2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -7v + 0.5 + v2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -7v + v2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -7v + v2 = 0 + 0.5 -7v + v2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -7v + v2 = 0.5 The v term is -7v. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7v + 12.25 + v2 = 0.5 + 12.25 Reorder the terms: 12.25 + -7v + v2 = 0.5 + 12.25 Combine like terms: 0.5 + 12.25 = 12.75 12.25 + -7v + v2 = 12.75 Factor a perfect square on the left side: (v + -3.5)(v + -3.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (v + -3.5) equal to 3.570714214 and -3.570714214.Subproblem 1
v + -3.5 = 3.570714214 Simplifying v + -3.5 = 3.570714214 Reorder the terms: -3.5 + v = 3.570714214 Solving -3.5 + v = 3.570714214 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = 3.570714214 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = 3.570714214 + 3.5 v = 3.570714214 + 3.5 Combine like terms: 3.570714214 + 3.5 = 7.070714214 v = 7.070714214 Simplifying v = 7.070714214Subproblem 2
v + -3.5 = -3.570714214 Simplifying v + -3.5 = -3.570714214 Reorder the terms: -3.5 + v = -3.570714214 Solving -3.5 + v = -3.570714214 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = -3.570714214 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = -3.570714214 + 3.5 v = -3.570714214 + 3.5 Combine like terms: -3.570714214 + 3.5 = -0.070714214 v = -0.070714214 Simplifying v = -0.070714214Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.070714214, -0.070714214}
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