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Simplifying 3w4 + 18w3 + -24w2 = 0 Reorder the terms: -24w2 + 18w3 + 3w4 = 0 Solving -24w2 + 18w3 + 3w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3w2'. 3w2(-8 + 6w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve: Simplifying w2 = 0 Solving w2 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w2 = 0 Take the square root of each side: w = {0}Subproblem 2
Set the factor '(-8 + 6w + w2)' equal to zero and attempt to solve: Simplifying -8 + 6w + w2 = 0 Solving -8 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 6w + 8 + w2 = 0 + 8 Reorder the terms: -8 + 8 + 6w + w2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6w + w2 = 0 + 8 6w + w2 = 0 + 8 Combine like terms: 0 + 8 = 8 6w + w2 = 8 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 = 8 + 9 Reorder the terms: 9 + 6w + w2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6w + w2 = 17 Factor a perfect square on the left side: (w + 3)(w + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (w + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
w + 3 = 4.123105626 Simplifying w + 3 = 4.123105626 Reorder the terms: 3 + w = 4.123105626 Solving 3 + w = 4.123105626 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 = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + w = 4.123105626 + -3 w = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 w = 1.123105626 Simplifying w = 1.123105626Subproblem 2
w + 3 = -4.123105626 Simplifying w + 3 = -4.123105626 Reorder the terms: 3 + w = -4.123105626 Solving 3 + w = -4.123105626 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 = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + w = -4.123105626 + -3 w = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 w = -7.123105626 Simplifying w = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.123105626, -7.123105626}Solution
w = {0, 1.123105626, -7.123105626}
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