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Simplifying 4w2 + 4w + -76 = 0 Reorder the terms: -76 + 4w + 4w2 = 0 Solving -76 + 4w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-19 + w + w2)' equal to zero and attempt to solve: Simplifying -19 + w + w2 = 0 Solving -19 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + w + 19 + w2 = 0 + 19 Reorder the terms: -19 + 19 + w + w2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + w + w2 = 0 + 19 w + w2 = 0 + 19 Combine like terms: 0 + 19 = 19 w + w2 = 19 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 19 + 0.25 Reorder the terms: 0.25 + w + w2 = 19 + 0.25 Combine like terms: 19 + 0.25 = 19.25 0.25 + w + w2 = 19.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (w + 0.5) equal to 4.387482194 and -4.387482194.Subproblem 1
w + 0.5 = 4.387482194 Simplifying w + 0.5 = 4.387482194 Reorder the terms: 0.5 + w = 4.387482194 Solving 0.5 + w = 4.387482194 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 4.387482194 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 4.387482194 + -0.5 w = 4.387482194 + -0.5 Combine like terms: 4.387482194 + -0.5 = 3.887482194 w = 3.887482194 Simplifying w = 3.887482194Subproblem 2
w + 0.5 = -4.387482194 Simplifying w + 0.5 = -4.387482194 Reorder the terms: 0.5 + w = -4.387482194 Solving 0.5 + w = -4.387482194 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -4.387482194 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -4.387482194 + -0.5 w = -4.387482194 + -0.5 Combine like terms: -4.387482194 + -0.5 = -4.887482194 w = -4.887482194 Simplifying w = -4.887482194Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.887482194, -4.887482194}Solution
w = {3.887482194, -4.887482194}
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