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Simplifying 8v2 + -2v + -8 = 0 Reorder the terms: -8 + -2v + 8v2 = 0 Solving -8 + -2v + 8v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -1v + 4v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1v + 4v2)' equal to zero and attempt to solve: Simplifying -4 + -1v + 4v2 = 0 Solving -4 + -1v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -0.25v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.25v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -0.25v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.25v + v2 = 0 + 1 -0.25v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.25v + v2 = 1 The v term is -0.25v. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25v + 0.015625 + v2 = 1 + 0.015625 Reorder the terms: 0.015625 + -0.25v + v2 = 1 + 0.015625 Combine like terms: 1 + 0.015625 = 1.015625 0.015625 + -0.25v + v2 = 1.015625 Factor a perfect square on the left side: (v + -0.125)(v + -0.125) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (v + -0.125) equal to 1.007782219 and -1.007782219.Subproblem 1
v + -0.125 = 1.007782219 Simplifying v + -0.125 = 1.007782219 Reorder the terms: -0.125 + v = 1.007782219 Solving -0.125 + v = 1.007782219 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + v = 1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + v = 1.007782219 + 0.125 v = 1.007782219 + 0.125 Combine like terms: 1.007782219 + 0.125 = 1.132782219 v = 1.132782219 Simplifying v = 1.132782219Subproblem 2
v + -0.125 = -1.007782219 Simplifying v + -0.125 = -1.007782219 Reorder the terms: -0.125 + v = -1.007782219 Solving -0.125 + v = -1.007782219 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + v = -1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + v = -1.007782219 + 0.125 v = -1.007782219 + 0.125 Combine like terms: -1.007782219 + 0.125 = -0.882782219 v = -0.882782219 Simplifying v = -0.882782219Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.132782219, -0.882782219}Solution
v = {1.132782219, -0.882782219}
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