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Simplifying 4v2 + -28v + 29 = 0 Reorder the terms: 29 + -28v + 4v2 = 0 Solving 29 + -28v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.25 + -7v + v2 = 0 Move the constant term to the right: Add '-7.25' to each side of the equation. 7.25 + -7v + -7.25 + v2 = 0 + -7.25 Reorder the terms: 7.25 + -7.25 + -7v + v2 = 0 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + -7v + v2 = 0 + -7.25 -7v + v2 = 0 + -7.25 Combine like terms: 0 + -7.25 = -7.25 -7v + v2 = -7.25 The v term is -7v. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7v + 12.25 + v2 = -7.25 + 12.25 Reorder the terms: 12.25 + -7v + v2 = -7.25 + 12.25 Combine like terms: -7.25 + 12.25 = 5 12.25 + -7v + v2 = 5 Factor a perfect square on the left side: (v + -3.5)(v + -3.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (v + -3.5) equal to 2.236067978 and -2.236067978.Subproblem 1
v + -3.5 = 2.236067978 Simplifying v + -3.5 = 2.236067978 Reorder the terms: -3.5 + v = 2.236067978 Solving -3.5 + v = 2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = 2.236067978 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = 2.236067978 + 3.5 v = 2.236067978 + 3.5 Combine like terms: 2.236067978 + 3.5 = 5.736067978 v = 5.736067978 Simplifying v = 5.736067978Subproblem 2
v + -3.5 = -2.236067978 Simplifying v + -3.5 = -2.236067978 Reorder the terms: -3.5 + v = -2.236067978 Solving -3.5 + v = -2.236067978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = -2.236067978 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = -2.236067978 + 3.5 v = -2.236067978 + 3.5 Combine like terms: -2.236067978 + 3.5 = 1.263932022 v = 1.263932022 Simplifying v = 1.263932022Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.736067978, 1.263932022}
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