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Simplifying 7w2 + 9w + -7 = 0 Reorder the terms: -7 + 9w + 7w2 = 0 Solving -7 + 9w + 7w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 1.285714286w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.285714286w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + 1.285714286w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.285714286w + w2 = 0 + 1 1.285714286w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.285714286w + w2 = 1 The w term is 1.285714286w. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286w + 0.4132653063 + w2 = 1 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286w + w2 = 1 + 0.4132653063 Combine like terms: 1 + 0.4132653063 = 1.4132653063 0.4132653063 + 1.285714286w + w2 = 1.4132653063 Factor a perfect square on the left side: (w + 0.642857143)(w + 0.642857143) = 1.4132653063 Calculate the square root of the right side: 1.188808356 Break this problem into two subproblems by setting (w + 0.642857143) equal to 1.188808356 and -1.188808356.Subproblem 1
w + 0.642857143 = 1.188808356 Simplifying w + 0.642857143 = 1.188808356 Reorder the terms: 0.642857143 + w = 1.188808356 Solving 0.642857143 + w = 1.188808356 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + w = 1.188808356 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + w = 1.188808356 + -0.642857143 w = 1.188808356 + -0.642857143 Combine like terms: 1.188808356 + -0.642857143 = 0.545951213 w = 0.545951213 Simplifying w = 0.545951213Subproblem 2
w + 0.642857143 = -1.188808356 Simplifying w + 0.642857143 = -1.188808356 Reorder the terms: 0.642857143 + w = -1.188808356 Solving 0.642857143 + w = -1.188808356 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + w = -1.188808356 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + w = -1.188808356 + -0.642857143 w = -1.188808356 + -0.642857143 Combine like terms: -1.188808356 + -0.642857143 = -1.831665499 w = -1.831665499 Simplifying w = -1.831665499Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.545951213, -1.831665499}
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