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Simplifying 3w2 + -8w + -42 = 0 Reorder the terms: -42 + -8w + 3w2 = 0 Solving -42 + -8w + 3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14 + -2.666666667w + w2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -2.666666667w + 14 + w2 = 0 + 14 Reorder the terms: -14 + 14 + -2.666666667w + w2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2.666666667w + w2 = 0 + 14 -2.666666667w + w2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2.666666667w + w2 = 14 The w term is -2.666666667w. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667w + 1.777777780 + w2 = 14 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667w + w2 = 14 + 1.777777780 Combine like terms: 14 + 1.777777780 = 15.77777778 1.777777780 + -2.666666667w + w2 = 15.77777778 Factor a perfect square on the left side: (w + -1.333333334)(w + -1.333333334) = 15.77777778 Calculate the square root of the right side: 3.972125096 Break this problem into two subproblems by setting (w + -1.333333334) equal to 3.972125096 and -3.972125096.Subproblem 1
w + -1.333333334 = 3.972125096 Simplifying w + -1.333333334 = 3.972125096 Reorder the terms: -1.333333334 + w = 3.972125096 Solving -1.333333334 + w = 3.972125096 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + w = 3.972125096 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + w = 3.972125096 + 1.333333334 w = 3.972125096 + 1.333333334 Combine like terms: 3.972125096 + 1.333333334 = 5.30545843 w = 5.30545843 Simplifying w = 5.30545843Subproblem 2
w + -1.333333334 = -3.972125096 Simplifying w + -1.333333334 = -3.972125096 Reorder the terms: -1.333333334 + w = -3.972125096 Solving -1.333333334 + w = -3.972125096 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + w = -3.972125096 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + w = -3.972125096 + 1.333333334 w = -3.972125096 + 1.333333334 Combine like terms: -3.972125096 + 1.333333334 = -2.638791762 w = -2.638791762 Simplifying w = -2.638791762Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.30545843, -2.638791762}
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