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Simplifying (w2 + -7w + -3) = 0 Reorder the terms: (-3 + -7w + w2) = 0 Remove parenthesis around (-3 + -7w + w2) -3 + -7w + w2 = 0 Solving -3 + -7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -7w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + -7w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7w + w2 = 0 + 3 -7w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 -7w + w2 = 3 The w term is -7w. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7w + 12.25 + w2 = 3 + 12.25 Reorder the terms: 12.25 + -7w + w2 = 3 + 12.25 Combine like terms: 3 + 12.25 = 15.25 12.25 + -7w + w2 = 15.25 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (w + -3.5) equal to 3.905124838 and -3.905124838.Subproblem 1
w + -3.5 = 3.905124838 Simplifying w + -3.5 = 3.905124838 Reorder the terms: -3.5 + w = 3.905124838 Solving -3.5 + w = 3.905124838 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = 3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = 3.905124838 + 3.5 w = 3.905124838 + 3.5 Combine like terms: 3.905124838 + 3.5 = 7.405124838 w = 7.405124838 Simplifying w = 7.405124838Subproblem 2
w + -3.5 = -3.905124838 Simplifying w + -3.5 = -3.905124838 Reorder the terms: -3.5 + w = -3.905124838 Solving -3.5 + w = -3.905124838 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = -3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = -3.905124838 + 3.5 w = -3.905124838 + 3.5 Combine like terms: -3.905124838 + 3.5 = -0.405124838 w = -0.405124838 Simplifying w = -0.405124838Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.405124838, -0.405124838}
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