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Simplifying -2v3(5v2 + 8v + -7) = 0 Reorder the terms: -2v3(-7 + 8v + 5v2) = 0 (-7 * -2v3 + 8v * -2v3 + 5v2 * -2v3) = 0 (14v3 + -16v4 + -10v5) = 0 Solving 14v3 + -16v4 + -10v5 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2v3'. 2v3(7 + -8v + -5v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'v3' equal to zero and attempt to solve: Simplifying v3 = 0 Solving v3 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7 + -8v + -5v2)' equal to zero and attempt to solve: Simplifying 7 + -8v + -5v2 = 0 Solving 7 + -8v + -5v2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + 1.6v + v2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 1.6v + 1.4 + v2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 1.6v + v2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 1.6v + v2 = 0 + 1.4 1.6v + v2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 1.6v + v2 = 1.4 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 = 1.4 + 0.64 Reorder the terms: 0.64 + 1.6v + v2 = 1.4 + 0.64 Combine like terms: 1.4 + 0.64 = 2.04 0.64 + 1.6v + v2 = 2.04 Factor a perfect square on the left side: (v + 0.8)(v + 0.8) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (v + 0.8) equal to 1.428285686 and -1.428285686.Subproblem 1
v + 0.8 = 1.428285686 Simplifying v + 0.8 = 1.428285686 Reorder the terms: 0.8 + v = 1.428285686 Solving 0.8 + v = 1.428285686 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 = 1.428285686 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = 1.428285686 + -0.8 v = 1.428285686 + -0.8 Combine like terms: 1.428285686 + -0.8 = 0.628285686 v = 0.628285686 Simplifying v = 0.628285686Subproblem 2
v + 0.8 = -1.428285686 Simplifying v + 0.8 = -1.428285686 Reorder the terms: 0.8 + v = -1.428285686 Solving 0.8 + v = -1.428285686 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 = -1.428285686 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = -1.428285686 + -0.8 v = -1.428285686 + -0.8 Combine like terms: -1.428285686 + -0.8 = -2.228285686 v = -2.228285686 Simplifying v = -2.228285686Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.628285686, -2.228285686}Solution
v = {0.628285686, -2.228285686}
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