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Simplifying 8v2 + 6v + -28 = -10 Reorder the terms: -28 + 6v + 8v2 = -10 Solving -28 + 6v + 8v2 = -10 Solving for variable 'v'. Reorder the terms: -28 + 10 + 6v + 8v2 = -10 + 10 Combine like terms: -28 + 10 = -18 -18 + 6v + 8v2 = -10 + 10 Combine like terms: -10 + 10 = 0 -18 + 6v + 8v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 3v + 4v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 3v + 4v2)' equal to zero and attempt to solve: Simplifying -9 + 3v + 4v2 = 0 Solving -9 + 3v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 0.75v + v2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.75v + 2.25 + v2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.75v + v2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.75v + v2 = 0 + 2.25 0.75v + v2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.75v + v2 = 2.25 The v term is 0.75v. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75v + 0.140625 + v2 = 2.25 + 0.140625 Reorder the terms: 0.140625 + 0.75v + v2 = 2.25 + 0.140625 Combine like terms: 2.25 + 0.140625 = 2.390625 0.140625 + 0.75v + v2 = 2.390625 Factor a perfect square on the left side: (v + 0.375)(v + 0.375) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (v + 0.375) equal to 1.54616461 and -1.54616461.Subproblem 1
v + 0.375 = 1.54616461 Simplifying v + 0.375 = 1.54616461 Reorder the terms: 0.375 + v = 1.54616461 Solving 0.375 + v = 1.54616461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + v = 1.54616461 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + v = 1.54616461 + -0.375 v = 1.54616461 + -0.375 Combine like terms: 1.54616461 + -0.375 = 1.17116461 v = 1.17116461 Simplifying v = 1.17116461Subproblem 2
v + 0.375 = -1.54616461 Simplifying v + 0.375 = -1.54616461 Reorder the terms: 0.375 + v = -1.54616461 Solving 0.375 + v = -1.54616461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + v = -1.54616461 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + v = -1.54616461 + -0.375 v = -1.54616461 + -0.375 Combine like terms: -1.54616461 + -0.375 = -1.92116461 v = -1.92116461 Simplifying v = -1.92116461Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.17116461, -1.92116461}Solution
v = {1.17116461, -1.92116461}
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