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Simplifying (7 + w) + -1(w + 7) * w = -4 Remove parenthesis around (7 + w) 7 + w + -1(w + 7) * w = -4 Reorder the terms: 7 + w + -1(7 + w) * w = -4 Reorder the terms for easier multiplication: 7 + w + -1w(7 + w) = -4 7 + w + (7 * -1w + w * -1w) = -4 7 + w + (-7w + -1w2) = -4 Combine like terms: w + -7w = -6w 7 + -6w + -1w2 = -4 Solving 7 + -6w + -1w2 = -4 Solving for variable 'w'. Reorder the terms: 7 + 4 + -6w + -1w2 = -4 + 4 Combine like terms: 7 + 4 = 11 11 + -6w + -1w2 = -4 + 4 Combine like terms: -4 + 4 = 0 11 + -6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 6w + w2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 6w + 11 + w2 = 0 + 11 Reorder the terms: -11 + 11 + 6w + w2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6w + w2 = 0 + 11 6w + w2 = 0 + 11 Combine like terms: 0 + 11 = 11 6w + w2 = 11 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 11 + 9 Reorder the terms: 9 + 6w + w2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + 6w + w2 = 20 Factor a perfect square on the left side: (w + 3)(w + 3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (w + 3) equal to 4.472135955 and -4.472135955.Subproblem 1
w + 3 = 4.472135955 Simplifying w + 3 = 4.472135955 Reorder the terms: 3 + w = 4.472135955 Solving 3 + w = 4.472135955 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + w = 4.472135955 + -3 w = 4.472135955 + -3 Combine like terms: 4.472135955 + -3 = 1.472135955 w = 1.472135955 Simplifying w = 1.472135955Subproblem 2
w + 3 = -4.472135955 Simplifying w + 3 = -4.472135955 Reorder the terms: 3 + w = -4.472135955 Solving 3 + w = -4.472135955 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + w = -4.472135955 + -3 w = -4.472135955 + -3 Combine like terms: -4.472135955 + -3 = -7.472135955 w = -7.472135955 Simplifying w = -7.472135955Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.472135955, -7.472135955}
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