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Simplifying -3v2 + 12v + 3 = 0 Reorder the terms: 3 + 12v + -3v2 = 0 Solving 3 + 12v + -3v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 4v + -1v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 4v + -1v2)' equal to zero and attempt to solve: Simplifying 1 + 4v + -1v2 = 0 Solving 1 + 4v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -4v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -4v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4v + v2 = 0 + 1 -4v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4v + v2 = 1 The v term is -4v. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4v + 4 + v2 = 1 + 4 Reorder the terms: 4 + -4v + v2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4v + v2 = 5 Factor a perfect square on the left side: (v + -2)(v + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (v + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
v + -2 = 2.236067978 Simplifying v + -2 = 2.236067978 Reorder the terms: -2 + v = 2.236067978 Solving -2 + v = 2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + v = 2.236067978 + 2 v = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 v = 4.236067978 Simplifying v = 4.236067978Subproblem 2
v + -2 = -2.236067978 Simplifying v + -2 = -2.236067978 Reorder the terms: -2 + v = -2.236067978 Solving -2 + v = -2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + v = -2.236067978 + 2 v = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 v = -0.236067978 Simplifying v = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.236067978, -0.236067978}Solution
v = {4.236067978, -0.236067978}
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