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Simplifying (3w2 + 3w) + -1(-8w2 + -3w + 8) = 0 Reorder the terms: (3w + 3w2) + -1(-8w2 + -3w + 8) = 0 Remove parenthesis around (3w + 3w2) 3w + 3w2 + -1(-8w2 + -3w + 8) = 0 Reorder the terms: 3w + 3w2 + -1(8 + -3w + -8w2) = 0 3w + 3w2 + (8 * -1 + -3w * -1 + -8w2 * -1) = 0 3w + 3w2 + (-8 + 3w + 8w2) = 0 Reorder the terms: -8 + 3w + 3w + 3w2 + 8w2 = 0 Combine like terms: 3w + 3w = 6w -8 + 6w + 3w2 + 8w2 = 0 Combine like terms: 3w2 + 8w2 = 11w2 -8 + 6w + 11w2 = 0 Solving -8 + 6w + 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 + 0.5454545455w + w2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 0.5454545455w + 0.7272727273 + w2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 0.5454545455w + w2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 0.5454545455w + w2 = 0 + 0.7272727273 0.5454545455w + w2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 0.5454545455w + w2 = 0.7272727273 The w term is 0.5454545455w. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455w + 0.07438016533 + w2 = 0.7272727273 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455w + w2 = 0.7272727273 + 0.07438016533 Combine like terms: 0.7272727273 + 0.07438016533 = 0.80165289263 0.07438016533 + 0.5454545455w + w2 = 0.80165289263 Factor a perfect square on the left side: (w + 0.2727272728)(w + 0.2727272728) = 0.80165289263 Calculate the square root of the right side: 0.895350709 Break this problem into two subproblems by setting (w + 0.2727272728) equal to 0.895350709 and -0.895350709.Subproblem 1
w + 0.2727272728 = 0.895350709 Simplifying w + 0.2727272728 = 0.895350709 Reorder the terms: 0.2727272728 + w = 0.895350709 Solving 0.2727272728 + w = 0.895350709 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + w = 0.895350709 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + w = 0.895350709 + -0.2727272728 w = 0.895350709 + -0.2727272728 Combine like terms: 0.895350709 + -0.2727272728 = 0.6226234362 w = 0.6226234362 Simplifying w = 0.6226234362Subproblem 2
w + 0.2727272728 = -0.895350709 Simplifying w + 0.2727272728 = -0.895350709 Reorder the terms: 0.2727272728 + w = -0.895350709 Solving 0.2727272728 + w = -0.895350709 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + w = -0.895350709 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + w = -0.895350709 + -0.2727272728 w = -0.895350709 + -0.2727272728 Combine like terms: -0.895350709 + -0.2727272728 = -1.1680779818 w = -1.1680779818 Simplifying w = -1.1680779818Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.6226234362, -1.1680779818}
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