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Simplifying (13w + 9)(4w + -3) = 9 Reorder the terms: (9 + 13w)(4w + -3) = 9 Reorder the terms: (9 + 13w)(-3 + 4w) = 9 Multiply (9 + 13w) * (-3 + 4w) (9(-3 + 4w) + 13w * (-3 + 4w)) = 9 ((-3 * 9 + 4w * 9) + 13w * (-3 + 4w)) = 9 ((-27 + 36w) + 13w * (-3 + 4w)) = 9 (-27 + 36w + (-3 * 13w + 4w * 13w)) = 9 (-27 + 36w + (-39w + 52w2)) = 9 Combine like terms: 36w + -39w = -3w (-27 + -3w + 52w2) = 9 Solving -27 + -3w + 52w2 = 9 Solving for variable 'w'. Reorder the terms: -27 + -9 + -3w + 52w2 = 9 + -9 Combine like terms: -27 + -9 = -36 -36 + -3w + 52w2 = 9 + -9 Combine like terms: 9 + -9 = 0 -36 + -3w + 52w2 = 0 Begin completing the square. Divide all terms by 52 the coefficient of the squared term: Divide each side by '52'. -0.6923076923 + -0.05769230769w + w2 = 0 Move the constant term to the right: Add '0.6923076923' to each side of the equation. -0.6923076923 + -0.05769230769w + 0.6923076923 + w2 = 0 + 0.6923076923 Reorder the terms: -0.6923076923 + 0.6923076923 + -0.05769230769w + w2 = 0 + 0.6923076923 Combine like terms: -0.6923076923 + 0.6923076923 = 0.0000000000 0.0000000000 + -0.05769230769w + w2 = 0 + 0.6923076923 -0.05769230769w + w2 = 0 + 0.6923076923 Combine like terms: 0 + 0.6923076923 = 0.6923076923 -0.05769230769w + w2 = 0.6923076923 The w term is -0.05769230769w. Take half its coefficient (-0.02884615385). Square it (0.0008321005919) and add it to both sides. Add '0.0008321005919' to each side of the equation. -0.05769230769w + 0.0008321005919 + w2 = 0.6923076923 + 0.0008321005919 Reorder the terms: 0.0008321005919 + -0.05769230769w + w2 = 0.6923076923 + 0.0008321005919 Combine like terms: 0.6923076923 + 0.0008321005919 = 0.6931397928919 0.0008321005919 + -0.05769230769w + w2 = 0.6931397928919 Factor a perfect square on the left side: (w + -0.02884615385)(w + -0.02884615385) = 0.6931397928919 Calculate the square root of the right side: 0.832550174 Break this problem into two subproblems by setting (w + -0.02884615385) equal to 0.832550174 and -0.832550174.Subproblem 1
w + -0.02884615385 = 0.832550174 Simplifying w + -0.02884615385 = 0.832550174 Reorder the terms: -0.02884615385 + w = 0.832550174 Solving -0.02884615385 + w = 0.832550174 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.02884615385' to each side of the equation. -0.02884615385 + 0.02884615385 + w = 0.832550174 + 0.02884615385 Combine like terms: -0.02884615385 + 0.02884615385 = 0.00000000000 0.00000000000 + w = 0.832550174 + 0.02884615385 w = 0.832550174 + 0.02884615385 Combine like terms: 0.832550174 + 0.02884615385 = 0.86139632785 w = 0.86139632785 Simplifying w = 0.86139632785Subproblem 2
w + -0.02884615385 = -0.832550174 Simplifying w + -0.02884615385 = -0.832550174 Reorder the terms: -0.02884615385 + w = -0.832550174 Solving -0.02884615385 + w = -0.832550174 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.02884615385' to each side of the equation. -0.02884615385 + 0.02884615385 + w = -0.832550174 + 0.02884615385 Combine like terms: -0.02884615385 + 0.02884615385 = 0.00000000000 0.00000000000 + w = -0.832550174 + 0.02884615385 w = -0.832550174 + 0.02884615385 Combine like terms: -0.832550174 + 0.02884615385 = -0.80370402015 w = -0.80370402015 Simplifying w = -0.80370402015Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.86139632785, -0.80370402015}
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