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Simplifying 9w2 + 7w2 + -10w + 15 = 1485 Reorder the terms: 15 + -10w + 9w2 + 7w2 = 1485 Combine like terms: 9w2 + 7w2 = 16w2 15 + -10w + 16w2 = 1485 Solving 15 + -10w + 16w2 = 1485 Solving for variable 'w'. Reorder the terms: 15 + -1485 + -10w + 16w2 = 1485 + -1485 Combine like terms: 15 + -1485 = -1470 -1470 + -10w + 16w2 = 1485 + -1485 Combine like terms: 1485 + -1485 = 0 -1470 + -10w + 16w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-735 + -5w + 8w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-735 + -5w + 8w2)' equal to zero and attempt to solve: Simplifying -735 + -5w + 8w2 = 0 Solving -735 + -5w + 8w2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -91.875 + -0.625w + w2 = 0 Move the constant term to the right: Add '91.875' to each side of the equation. -91.875 + -0.625w + 91.875 + w2 = 0 + 91.875 Reorder the terms: -91.875 + 91.875 + -0.625w + w2 = 0 + 91.875 Combine like terms: -91.875 + 91.875 = 0.000 0.000 + -0.625w + w2 = 0 + 91.875 -0.625w + w2 = 0 + 91.875 Combine like terms: 0 + 91.875 = 91.875 -0.625w + w2 = 91.875 The w term is -0.625w. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625w + 0.09765625 + w2 = 91.875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625w + w2 = 91.875 + 0.09765625 Combine like terms: 91.875 + 0.09765625 = 91.97265625 0.09765625 + -0.625w + w2 = 91.97265625 Factor a perfect square on the left side: (w + -0.3125)(w + -0.3125) = 91.97265625 Calculate the square root of the right side: 9.590237549 Break this problem into two subproblems by setting (w + -0.3125) equal to 9.590237549 and -9.590237549.Subproblem 1
w + -0.3125 = 9.590237549 Simplifying w + -0.3125 = 9.590237549 Reorder the terms: -0.3125 + w = 9.590237549 Solving -0.3125 + w = 9.590237549 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + w = 9.590237549 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + w = 9.590237549 + 0.3125 w = 9.590237549 + 0.3125 Combine like terms: 9.590237549 + 0.3125 = 9.902737549 w = 9.902737549 Simplifying w = 9.902737549Subproblem 2
w + -0.3125 = -9.590237549 Simplifying w + -0.3125 = -9.590237549 Reorder the terms: -0.3125 + w = -9.590237549 Solving -0.3125 + w = -9.590237549 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + w = -9.590237549 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + w = -9.590237549 + 0.3125 w = -9.590237549 + 0.3125 Combine like terms: -9.590237549 + 0.3125 = -9.277737549 w = -9.277737549 Simplifying w = -9.277737549Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.902737549, -9.277737549}Solution
w = {9.902737549, -9.277737549}
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