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Simplifying w2 + 8.3w + -73.6 = 0 Reorder the terms: -73.6 + 8.3w + w2 = 0 Solving -73.6 + 8.3w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '73.6' to each side of the equation. -73.6 + 8.3w + 73.6 + w2 = 0 + 73.6 Reorder the terms: -73.6 + 73.6 + 8.3w + w2 = 0 + 73.6 Combine like terms: -73.6 + 73.6 = 0.0 0.0 + 8.3w + w2 = 0 + 73.6 8.3w + w2 = 0 + 73.6 Combine like terms: 0 + 73.6 = 73.6 8.3w + w2 = 73.6 The w term is 8.3w. Take half its coefficient (4.15). Square it (17.2225) and add it to both sides. Add '17.2225' to each side of the equation. 8.3w + 17.2225 + w2 = 73.6 + 17.2225 Reorder the terms: 17.2225 + 8.3w + w2 = 73.6 + 17.2225 Combine like terms: 73.6 + 17.2225 = 90.8225 17.2225 + 8.3w + w2 = 90.8225 Factor a perfect square on the left side: (w + 4.15)(w + 4.15) = 90.8225 Calculate the square root of the right side: 9.530083945 Break this problem into two subproblems by setting (w + 4.15) equal to 9.530083945 and -9.530083945.Subproblem 1
w + 4.15 = 9.530083945 Simplifying w + 4.15 = 9.530083945 Reorder the terms: 4.15 + w = 9.530083945 Solving 4.15 + w = 9.530083945 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.15' to each side of the equation. 4.15 + -4.15 + w = 9.530083945 + -4.15 Combine like terms: 4.15 + -4.15 = 0.00 0.00 + w = 9.530083945 + -4.15 w = 9.530083945 + -4.15 Combine like terms: 9.530083945 + -4.15 = 5.380083945 w = 5.380083945 Simplifying w = 5.380083945Subproblem 2
w + 4.15 = -9.530083945 Simplifying w + 4.15 = -9.530083945 Reorder the terms: 4.15 + w = -9.530083945 Solving 4.15 + w = -9.530083945 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.15' to each side of the equation. 4.15 + -4.15 + w = -9.530083945 + -4.15 Combine like terms: 4.15 + -4.15 = 0.00 0.00 + w = -9.530083945 + -4.15 w = -9.530083945 + -4.15 Combine like terms: -9.530083945 + -4.15 = -13.680083945 w = -13.680083945 Simplifying w = -13.680083945Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.380083945, -13.680083945}
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