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Simplifying (9w2 + 7w) + -1(-2w2 + -5w + 8) = 0 Reorder the terms: (7w + 9w2) + -1(-2w2 + -5w + 8) = 0 Remove parenthesis around (7w + 9w2) 7w + 9w2 + -1(-2w2 + -5w + 8) = 0 Reorder the terms: 7w + 9w2 + -1(8 + -5w + -2w2) = 0 7w + 9w2 + (8 * -1 + -5w * -1 + -2w2 * -1) = 0 7w + 9w2 + (-8 + 5w + 2w2) = 0 Reorder the terms: -8 + 7w + 5w + 9w2 + 2w2 = 0 Combine like terms: 7w + 5w = 12w -8 + 12w + 9w2 + 2w2 = 0 Combine like terms: 9w2 + 2w2 = 11w2 -8 + 12w + 11w2 = 0 Solving -8 + 12w + 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'. -0.7272727273 + 1.090909091w + w2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 1.090909091w + 0.7272727273 + w2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 1.090909091w + w2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 1.090909091w + w2 = 0 + 0.7272727273 1.090909091w + w2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 1.090909091w + w2 = 0.7272727273 The w term is 1.090909091w. Take half its coefficient (0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. 1.090909091w + 0.2975206612 + w2 = 0.7272727273 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091w + w2 = 0.7272727273 + 0.2975206612 Combine like terms: 0.7272727273 + 0.2975206612 = 1.0247933885 0.2975206612 + 1.090909091w + w2 = 1.0247933885 Factor a perfect square on the left side: (w + 0.5454545455)(w + 0.5454545455) = 1.0247933885 Calculate the square root of the right side: 1.012320793 Break this problem into two subproblems by setting (w + 0.5454545455) equal to 1.012320793 and -1.012320793.Subproblem 1
w + 0.5454545455 = 1.012320793 Simplifying w + 0.5454545455 = 1.012320793 Reorder the terms: 0.5454545455 + w = 1.012320793 Solving 0.5454545455 + w = 1.012320793 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + w = 1.012320793 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + w = 1.012320793 + -0.5454545455 w = 1.012320793 + -0.5454545455 Combine like terms: 1.012320793 + -0.5454545455 = 0.4668662475 w = 0.4668662475 Simplifying w = 0.4668662475Subproblem 2
w + 0.5454545455 = -1.012320793 Simplifying w + 0.5454545455 = -1.012320793 Reorder the terms: 0.5454545455 + w = -1.012320793 Solving 0.5454545455 + w = -1.012320793 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + w = -1.012320793 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + w = -1.012320793 + -0.5454545455 w = -1.012320793 + -0.5454545455 Combine like terms: -1.012320793 + -0.5454545455 = -1.5577753385 w = -1.5577753385 Simplifying w = -1.5577753385Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.4668662475, -1.5577753385}
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