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Simplifying (4w2 + -7w + 3) + (-6w2 + w + 2) = 0 Reorder the terms: (3 + -7w + 4w2) + (-6w2 + w + 2) = 0 Remove parenthesis around (3 + -7w + 4w2) 3 + -7w + 4w2 + (-6w2 + w + 2) = 0 Reorder the terms: 3 + -7w + 4w2 + (2 + w + -6w2) = 0 Remove parenthesis around (2 + w + -6w2) 3 + -7w + 4w2 + 2 + w + -6w2 = 0 Reorder the terms: 3 + 2 + -7w + w + 4w2 + -6w2 = 0 Combine like terms: 3 + 2 = 5 5 + -7w + w + 4w2 + -6w2 = 0 Combine like terms: -7w + w = -6w 5 + -6w + 4w2 + -6w2 = 0 Combine like terms: 4w2 + -6w2 = -2w2 5 + -6w + -2w2 = 0 Solving 5 + -6w + -2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + 3w + w2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 3w + 2.5 + w2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 3w + w2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 3w + w2 = 0 + 2.5 3w + w2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 3w + w2 = 2.5 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 2.5 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + 3w + w2 = 4.75 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (w + 1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
w + 1.5 = 2.179449472 Simplifying w + 1.5 = 2.179449472 Reorder the terms: 1.5 + w = 2.179449472 Solving 1.5 + w = 2.179449472 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 2.179449472 + -1.5 w = 2.179449472 + -1.5 Combine like terms: 2.179449472 + -1.5 = 0.679449472 w = 0.679449472 Simplifying w = 0.679449472Subproblem 2
w + 1.5 = -2.179449472 Simplifying w + 1.5 = -2.179449472 Reorder the terms: 1.5 + w = -2.179449472 Solving 1.5 + w = -2.179449472 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -2.179449472 + -1.5 w = -2.179449472 + -1.5 Combine like terms: -2.179449472 + -1.5 = -3.679449472 w = -3.679449472 Simplifying w = -3.679449472Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.679449472, -3.679449472}
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