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Simplifying 3w2 + 24w + -3 = 0 Reorder the terms: -3 + 24w + 3w2 = 0 Solving -3 + 24w + 3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 8w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 8w + w2)' equal to zero and attempt to solve: Simplifying -1 + 8w + w2 = 0 Solving -1 + 8w + w2 = 0 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 = 0.123105626 w = 0.123105626 Simplifying w = 0.123105626Subproblem 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 = -8.123105626 w = -8.123105626 Simplifying w = -8.123105626Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.123105626, -8.123105626}Solution
w = {0.123105626, -8.123105626}
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