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Simplifying 11w2 + -3w + -42 = 0 Reorder the terms: -42 + -3w + 11w2 = 0 Solving -42 + -3w + 11w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -3.818181818 + -0.2727272727w + w2 = 0 Move the constant term to the right: Add '3.818181818' to each side of the equation. -3.818181818 + -0.2727272727w + 3.818181818 + w2 = 0 + 3.818181818 Reorder the terms: -3.818181818 + 3.818181818 + -0.2727272727w + w2 = 0 + 3.818181818 Combine like terms: -3.818181818 + 3.818181818 = 0.000000000 0.000000000 + -0.2727272727w + w2 = 0 + 3.818181818 -0.2727272727w + w2 = 0 + 3.818181818 Combine like terms: 0 + 3.818181818 = 3.818181818 -0.2727272727w + w2 = 3.818181818 The w term is -0.2727272727w. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727w + 0.01859504133 + w2 = 3.818181818 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727w + w2 = 3.818181818 + 0.01859504133 Combine like terms: 3.818181818 + 0.01859504133 = 3.83677685933 0.01859504133 + -0.2727272727w + w2 = 3.83677685933 Factor a perfect square on the left side: (w + -0.1363636364)(w + -0.1363636364) = 3.83677685933 Calculate the square root of the right side: 1.958769221 Break this problem into two subproblems by setting (w + -0.1363636364) equal to 1.958769221 and -1.958769221.Subproblem 1
w + -0.1363636364 = 1.958769221 Simplifying w + -0.1363636364 = 1.958769221 Reorder the terms: -0.1363636364 + w = 1.958769221 Solving -0.1363636364 + w = 1.958769221 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + w = 1.958769221 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + w = 1.958769221 + 0.1363636364 w = 1.958769221 + 0.1363636364 Combine like terms: 1.958769221 + 0.1363636364 = 2.0951328574 w = 2.0951328574 Simplifying w = 2.0951328574Subproblem 2
w + -0.1363636364 = -1.958769221 Simplifying w + -0.1363636364 = -1.958769221 Reorder the terms: -0.1363636364 + w = -1.958769221 Solving -0.1363636364 + w = -1.958769221 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + w = -1.958769221 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + w = -1.958769221 + 0.1363636364 w = -1.958769221 + 0.1363636364 Combine like terms: -1.958769221 + 0.1363636364 = -1.8224055846 w = -1.8224055846 Simplifying w = -1.8224055846Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.0951328574, -1.8224055846}
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