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Simplifying (-3w2 + 7w + -4) + (w2 + 2w + 6) = 0 Reorder the terms: (-4 + 7w + -3w2) + (w2 + 2w + 6) = 0 Remove parenthesis around (-4 + 7w + -3w2) -4 + 7w + -3w2 + (w2 + 2w + 6) = 0 Reorder the terms: -4 + 7w + -3w2 + (6 + 2w + w2) = 0 Remove parenthesis around (6 + 2w + w2) -4 + 7w + -3w2 + 6 + 2w + w2 = 0 Reorder the terms: -4 + 6 + 7w + 2w + -3w2 + w2 = 0 Combine like terms: -4 + 6 = 2 2 + 7w + 2w + -3w2 + w2 = 0 Combine like terms: 7w + 2w = 9w 2 + 9w + -3w2 + w2 = 0 Combine like terms: -3w2 + w2 = -2w2 2 + 9w + -2w2 = 0 Solving 2 + 9w + -2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + -4.5w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.5w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -4.5w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.5w + w2 = 0 + 1 -4.5w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.5w + w2 = 1 The w term is -4.5w. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5w + 5.0625 + w2 = 1 + 5.0625 Reorder the terms: 5.0625 + -4.5w + w2 = 1 + 5.0625 Combine like terms: 1 + 5.0625 = 6.0625 5.0625 + -4.5w + w2 = 6.0625 Factor a perfect square on the left side: (w + -2.25)(w + -2.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (w + -2.25) equal to 2.46221445 and -2.46221445.Subproblem 1
w + -2.25 = 2.46221445 Simplifying w + -2.25 = 2.46221445 Reorder the terms: -2.25 + w = 2.46221445 Solving -2.25 + w = 2.46221445 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + w = 2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + w = 2.46221445 + 2.25 w = 2.46221445 + 2.25 Combine like terms: 2.46221445 + 2.25 = 4.71221445 w = 4.71221445 Simplifying w = 4.71221445Subproblem 2
w + -2.25 = -2.46221445 Simplifying w + -2.25 = -2.46221445 Reorder the terms: -2.25 + w = -2.46221445 Solving -2.25 + w = -2.46221445 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + w = -2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + w = -2.46221445 + 2.25 w = -2.46221445 + 2.25 Combine like terms: -2.46221445 + 2.25 = -0.21221445 w = -0.21221445 Simplifying w = -0.21221445Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.71221445, -0.21221445}
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