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Simplifying 18w2 + 18w + -7 = 0 Reorder the terms: -7 + 18w + 18w2 = 0 Solving -7 + 18w + 18w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3888888889 + w + w2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + w + 0.3888888889 + w2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + w + w2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + w + w2 = 0 + 0.3888888889 w + w2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 w + w2 = 0.3888888889 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + w2 = 0.3888888889 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + w2 = 0.3888888889 + 0.25 Combine like terms: 0.3888888889 + 0.25 = 0.6388888889 1.25 + w2 = 0.6388888889 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 0.6388888889 Calculate the square root of the right side: 0.799305254 Break this problem into two subproblems by setting (w + 0.5) equal to 0.799305254 and -0.799305254.Subproblem 1
w + 0.5 = 0.799305254 Simplifying w + 0.5 = 0.799305254 Reorder the terms: 0.5 + w = 0.799305254 Solving 0.5 + w = 0.799305254 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 0.799305254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 0.799305254 + -0.5 w = 0.799305254 + -0.5 Combine like terms: 0.799305254 + -0.5 = 0.299305254 w = 0.299305254 Simplifying w = 0.299305254Subproblem 2
w + 0.5 = -0.799305254 Simplifying w + 0.5 = -0.799305254 Reorder the terms: 0.5 + w = -0.799305254 Solving 0.5 + w = -0.799305254 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -0.799305254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -0.799305254 + -0.5 w = -0.799305254 + -0.5 Combine like terms: -0.799305254 + -0.5 = -1.299305254 w = -1.299305254 Simplifying w = -1.299305254Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.299305254, -1.299305254}
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