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Simplifying 4w2 + 12w + -44 = 0 Reorder the terms: -44 + 12w + 4w2 = 0 Solving -44 + 12w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + 3w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + 3w + w2)' equal to zero and attempt to solve: Simplifying -11 + 3w + w2 = 0 Solving -11 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 3w + 11 + w2 = 0 + 11 Reorder the terms: -11 + 11 + 3w + w2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 3w + w2 = 0 + 11 3w + w2 = 0 + 11 Combine like terms: 0 + 11 = 11 3w + w2 = 11 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 = 11 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 11 + 2.25 Combine like terms: 11 + 2.25 = 13.25 2.25 + 3w + w2 = 13.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (w + 1.5) equal to 3.640054945 and -3.640054945.Subproblem 1
w + 1.5 = 3.640054945 Simplifying w + 1.5 = 3.640054945 Reorder the terms: 1.5 + w = 3.640054945 Solving 1.5 + w = 3.640054945 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 = 3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 3.640054945 + -1.5 w = 3.640054945 + -1.5 Combine like terms: 3.640054945 + -1.5 = 2.140054945 w = 2.140054945 Simplifying w = 2.140054945Subproblem 2
w + 1.5 = -3.640054945 Simplifying w + 1.5 = -3.640054945 Reorder the terms: 1.5 + w = -3.640054945 Solving 1.5 + w = -3.640054945 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 = -3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -3.640054945 + -1.5 w = -3.640054945 + -1.5 Combine like terms: -3.640054945 + -1.5 = -5.140054945 w = -5.140054945 Simplifying w = -5.140054945Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.140054945, -5.140054945}Solution
w = {2.140054945, -5.140054945}
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