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Simplifying (-3w2 + w + -4) + (5w2 + 7w + 2) = 0 Reorder the terms: (-4 + w + -3w2) + (5w2 + 7w + 2) = 0 Remove parenthesis around (-4 + w + -3w2) -4 + w + -3w2 + (5w2 + 7w + 2) = 0 Reorder the terms: -4 + w + -3w2 + (2 + 7w + 5w2) = 0 Remove parenthesis around (2 + 7w + 5w2) -4 + w + -3w2 + 2 + 7w + 5w2 = 0 Reorder the terms: -4 + 2 + w + 7w + -3w2 + 5w2 = 0 Combine like terms: -4 + 2 = -2 -2 + w + 7w + -3w2 + 5w2 = 0 Combine like terms: w + 7w = 8w -2 + 8w + -3w2 + 5w2 = 0 Combine like terms: -3w2 + 5w2 = 2w2 -2 + 8w + 2w2 = 0 Solving -2 + 8w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 4w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 4w + w2)' equal to zero and attempt to solve: Simplifying -1 + 4w + w2 = 0 Solving -1 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 4w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + 4w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4w + w2 = 0 + 1 4w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 4w + w2 = 1 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 1 + 4 Reorder the terms: 4 + 4w + w2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4w + w2 = 5 Factor a perfect square on the left side: (w + 2)(w + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (w + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
w + 2 = 2.236067978 Simplifying w + 2 = 2.236067978 Reorder the terms: 2 + w = 2.236067978 Solving 2 + w = 2.236067978 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + w = 2.236067978 + -2 w = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 w = 0.236067978 Simplifying w = 0.236067978Subproblem 2
w + 2 = -2.236067978 Simplifying w + 2 = -2.236067978 Reorder the terms: 2 + w = -2.236067978 Solving 2 + w = -2.236067978 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + w = -2.236067978 + -2 w = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 w = -4.236067978 Simplifying w = -4.236067978Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.236067978, -4.236067978}Solution
w = {0.236067978, -4.236067978}
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