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Simplifying (4w2 + -6w + -5) + -1(3w2 + 2w + -4) = 0 Reorder the terms: (-5 + -6w + 4w2) + -1(3w2 + 2w + -4) = 0 Remove parenthesis around (-5 + -6w + 4w2) -5 + -6w + 4w2 + -1(3w2 + 2w + -4) = 0 Reorder the terms: -5 + -6w + 4w2 + -1(-4 + 2w + 3w2) = 0 -5 + -6w + 4w2 + (-4 * -1 + 2w * -1 + 3w2 * -1) = 0 -5 + -6w + 4w2 + (4 + -2w + -3w2) = 0 Reorder the terms: -5 + 4 + -6w + -2w + 4w2 + -3w2 = 0 Combine like terms: -5 + 4 = -1 -1 + -6w + -2w + 4w2 + -3w2 = 0 Combine like terms: -6w + -2w = -8w -1 + -8w + 4w2 + -3w2 = 0 Combine like terms: 4w2 + -3w2 = 1w2 -1 + -8w + 1w2 = 0 Solving -1 + -8w + 1w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -8w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -8w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8w + w2 = 0 + 1 -8w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8w + w2 = 1 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = 1 + 16 Reorder the terms: 16 + -8w + w2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + -8w + w2 = 17 Factor a perfect square on the left side: (w + -4)(w + -4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (w + -4) equal to 4.123105626 and -4.123105626.Subproblem 1
w + -4 = 4.123105626 Simplifying w + -4 = 4.123105626 Reorder the terms: -4 + w = 4.123105626 Solving -4 + w = 4.123105626 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + w = 4.123105626 + 4 w = 4.123105626 + 4 Combine like terms: 4.123105626 + 4 = 8.123105626 w = 8.123105626 Simplifying w = 8.123105626Subproblem 2
w + -4 = -4.123105626 Simplifying w + -4 = -4.123105626 Reorder the terms: -4 + w = -4.123105626 Solving -4 + w = -4.123105626 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + w = -4.123105626 + 4 w = -4.123105626 + 4 Combine like terms: -4.123105626 + 4 = -0.123105626 w = -0.123105626 Simplifying w = -0.123105626Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.123105626, -0.123105626}
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