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Simplifying -4v2 + -8v + 20 = 0 Reorder the terms: 20 + -8v + -4v2 = 0 Solving 20 + -8v + -4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -2v + -1v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -2v + -1v2)' equal to zero and attempt to solve: Simplifying 5 + -2v + -1v2 = 0 Solving 5 + -2v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 2v + v2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2v + 5 + v2 = 0 + 5 Reorder the terms: -5 + 5 + 2v + v2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2v + v2 = 0 + 5 2v + v2 = 0 + 5 Combine like terms: 0 + 5 = 5 2v + v2 = 5 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 5 + 1 Reorder the terms: 1 + 2v + v2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2v + v2 = 6 Factor a perfect square on the left side: (v + 1)(v + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (v + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
v + 1 = 2.449489743 Simplifying v + 1 = 2.449489743 Reorder the terms: 1 + v = 2.449489743 Solving 1 + v = 2.449489743 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + v = 2.449489743 + -1 v = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 v = 1.449489743 Simplifying v = 1.449489743Subproblem 2
v + 1 = -2.449489743 Simplifying v + 1 = -2.449489743 Reorder the terms: 1 + v = -2.449489743 Solving 1 + v = -2.449489743 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + v = -2.449489743 + -1 v = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 v = -3.449489743 Simplifying v = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.449489743, -3.449489743}Solution
v = {1.449489743, -3.449489743}
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