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Simplifying 5w2 + 12w + -192 = 0 Reorder the terms: -192 + 12w + 5w2 = 0 Solving -192 + 12w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -38.4 + 2.4w + w2 = 0 Move the constant term to the right: Add '38.4' to each side of the equation. -38.4 + 2.4w + 38.4 + w2 = 0 + 38.4 Reorder the terms: -38.4 + 38.4 + 2.4w + w2 = 0 + 38.4 Combine like terms: -38.4 + 38.4 = 0.0 0.0 + 2.4w + w2 = 0 + 38.4 2.4w + w2 = 0 + 38.4 Combine like terms: 0 + 38.4 = 38.4 2.4w + w2 = 38.4 The w term is 2.4w. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4w + 1.44 + w2 = 38.4 + 1.44 Reorder the terms: 1.44 + 2.4w + w2 = 38.4 + 1.44 Combine like terms: 38.4 + 1.44 = 39.84 1.44 + 2.4w + w2 = 39.84 Factor a perfect square on the left side: (w + 1.2)(w + 1.2) = 39.84 Calculate the square root of the right side: 6.311893535 Break this problem into two subproblems by setting (w + 1.2) equal to 6.311893535 and -6.311893535.Subproblem 1
w + 1.2 = 6.311893535 Simplifying w + 1.2 = 6.311893535 Reorder the terms: 1.2 + w = 6.311893535 Solving 1.2 + w = 6.311893535 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + w = 6.311893535 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + w = 6.311893535 + -1.2 w = 6.311893535 + -1.2 Combine like terms: 6.311893535 + -1.2 = 5.111893535 w = 5.111893535 Simplifying w = 5.111893535Subproblem 2
w + 1.2 = -6.311893535 Simplifying w + 1.2 = -6.311893535 Reorder the terms: 1.2 + w = -6.311893535 Solving 1.2 + w = -6.311893535 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + w = -6.311893535 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + w = -6.311893535 + -1.2 w = -6.311893535 + -1.2 Combine like terms: -6.311893535 + -1.2 = -7.511893535 w = -7.511893535 Simplifying w = -7.511893535Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.111893535, -7.511893535}
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