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Simplifying (4w2 + -6w + -3) = 0 Reorder the terms: (-3 + -6w + 4w2) = 0 Remove parenthesis around (-3 + -6w + 4w2) -3 + -6w + 4w2 = 0 Solving -3 + -6w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -1.5w + w2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.5w + 0.75 + w2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.5w + w2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.5w + w2 = 0 + 0.75 -1.5w + w2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.5w + w2 = 0.75 The w term is -1.5w. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5w + 0.5625 + w2 = 0.75 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = 0.75 + 0.5625 Combine like terms: 0.75 + 0.5625 = 1.3125 0.5625 + -1.5w + w2 = 1.3125 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (w + -0.75) equal to 1.145643924 and -1.145643924.Subproblem 1
w + -0.75 = 1.145643924 Simplifying w + -0.75 = 1.145643924 Reorder the terms: -0.75 + w = 1.145643924 Solving -0.75 + w = 1.145643924 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = 1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = 1.145643924 + 0.75 w = 1.145643924 + 0.75 Combine like terms: 1.145643924 + 0.75 = 1.895643924 w = 1.895643924 Simplifying w = 1.895643924Subproblem 2
w + -0.75 = -1.145643924 Simplifying w + -0.75 = -1.145643924 Reorder the terms: -0.75 + w = -1.145643924 Solving -0.75 + w = -1.145643924 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = -1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = -1.145643924 + 0.75 w = -1.145643924 + 0.75 Combine like terms: -1.145643924 + 0.75 = -0.395643924 w = -0.395643924 Simplifying w = -0.395643924Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.895643924, -0.395643924}
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