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Simplifying (-7w2 + -6w + 1) + (-3w2 + 2) = 0 Reorder the terms: (1 + -6w + -7w2) + (-3w2 + 2) = 0 Remove parenthesis around (1 + -6w + -7w2) 1 + -6w + -7w2 + (-3w2 + 2) = 0 Reorder the terms: 1 + -6w + -7w2 + (2 + -3w2) = 0 Remove parenthesis around (2 + -3w2) 1 + -6w + -7w2 + 2 + -3w2 = 0 Reorder the terms: 1 + 2 + -6w + -7w2 + -3w2 = 0 Combine like terms: 1 + 2 = 3 3 + -6w + -7w2 + -3w2 = 0 Combine like terms: -7w2 + -3w2 = -10w2 3 + -6w + -10w2 = 0 Solving 3 + -6w + -10w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + 0.6w + w2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.6w + 0.3 + w2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.6w + w2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.6w + w2 = 0.0 + 0.3 0.6w + w2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 0.6w + w2 = 0.3 The w term is 0.6w. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6w + 0.09 + w2 = 0.3 + 0.09 Reorder the terms: 0.09 + 0.6w + w2 = 0.3 + 0.09 Combine like terms: 0.3 + 0.09 = 0.39 0.09 + 0.6w + w2 = 0.39 Factor a perfect square on the left side: (w + 0.3)(w + 0.3) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (w + 0.3) equal to 0.6244998 and -0.6244998.Subproblem 1
w + 0.3 = 0.6244998 Simplifying w + 0.3 = 0.6244998 Reorder the terms: 0.3 + w = 0.6244998 Solving 0.3 + w = 0.6244998 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + w = 0.6244998 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + w = 0.6244998 + -0.3 w = 0.6244998 + -0.3 Combine like terms: 0.6244998 + -0.3 = 0.3244998 w = 0.3244998 Simplifying w = 0.3244998Subproblem 2
w + 0.3 = -0.6244998 Simplifying w + 0.3 = -0.6244998 Reorder the terms: 0.3 + w = -0.6244998 Solving 0.3 + w = -0.6244998 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + w = -0.6244998 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + w = -0.6244998 + -0.3 w = -0.6244998 + -0.3 Combine like terms: -0.6244998 + -0.3 = -0.9244998 w = -0.9244998 Simplifying w = -0.9244998Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.3244998, -0.9244998}
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