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Simplifying w + 2w2 = 146 Solving w + 2w2 = 146 Solving for variable 'w'. Reorder the terms: -146 + w + 2w2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -73 + 0.5w + w2 = 0 Move the constant term to the right: Add '73' to each side of the equation. -73 + 0.5w + 73 + w2 = 0 + 73 Reorder the terms: -73 + 73 + 0.5w + w2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 0.5w + w2 = 0 + 73 0.5w + w2 = 0 + 73 Combine like terms: 0 + 73 = 73 0.5w + w2 = 73 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. 0.5w + 0.25 + w2 = 73 + 0.25 Reorder the terms: 0.25 + 0.5w + w2 = 73 + 0.25 Combine like terms: 73 + 0.25 = 73.25 0.25 + 0.5w + w2 = 73.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 73.25 Calculate the square root of the right side: 8.558621384 Break this problem into two subproblems by setting (w + 0.5) equal to 8.558621384 and -8.558621384.Subproblem 1
w + 0.5 = 8.558621384 Simplifying w + 0.5 = 8.558621384 Reorder the terms: 0.5 + w = 8.558621384 Solving 0.5 + w = 8.558621384 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 = 8.558621384 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 8.558621384 + -0.5 w = 8.558621384 + -0.5 Combine like terms: 8.558621384 + -0.5 = 8.058621384 w = 8.058621384 Simplifying w = 8.058621384Subproblem 2
w + 0.5 = -8.558621384 Simplifying w + 0.5 = -8.558621384 Reorder the terms: 0.5 + w = -8.558621384 Solving 0.5 + w = -8.558621384 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 = -8.558621384 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -8.558621384 + -0.5 w = -8.558621384 + -0.5 Combine like terms: -8.558621384 + -0.5 = -9.058621384 w = -9.058621384 Simplifying w = -9.058621384Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.058621384, -9.058621384}
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