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Simplifying (7w2 + -2w + 9) + (-4w2 + 8w + -13) = 0 Reorder the terms: (9 + -2w + 7w2) + (-4w2 + 8w + -13) = 0 Remove parenthesis around (9 + -2w + 7w2) 9 + -2w + 7w2 + (-4w2 + 8w + -13) = 0 Reorder the terms: 9 + -2w + 7w2 + (-13 + 8w + -4w2) = 0 Remove parenthesis around (-13 + 8w + -4w2) 9 + -2w + 7w2 + -13 + 8w + -4w2 = 0 Reorder the terms: 9 + -13 + -2w + 8w + 7w2 + -4w2 = 0 Combine like terms: 9 + -13 = -4 -4 + -2w + 8w + 7w2 + -4w2 = 0 Combine like terms: -2w + 8w = 6w -4 + 6w + 7w2 + -4w2 = 0 Combine like terms: 7w2 + -4w2 = 3w2 -4 + 6w + 3w2 = 0 Solving -4 + 6w + 3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 2w + w2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 2w + 1.333333333 + w2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 2w + w2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 2w + w2 = 0 + 1.333333333 2w + w2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 2w + w2 = 1.333333333 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 1.333333333 + 1 Reorder the terms: 1 + 2w + w2 = 1.333333333 + 1 Combine like terms: 1.333333333 + 1 = 2.333333333 1 + 2w + w2 = 2.333333333 Factor a perfect square on the left side: (w + 1)(w + 1) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (w + 1) equal to 1.527525232 and -1.527525232.Subproblem 1
w + 1 = 1.527525232 Simplifying w + 1 = 1.527525232 Reorder the terms: 1 + w = 1.527525232 Solving 1 + w = 1.527525232 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + w = 1.527525232 + -1 w = 1.527525232 + -1 Combine like terms: 1.527525232 + -1 = 0.527525232 w = 0.527525232 Simplifying w = 0.527525232Subproblem 2
w + 1 = -1.527525232 Simplifying w + 1 = -1.527525232 Reorder the terms: 1 + w = -1.527525232 Solving 1 + w = -1.527525232 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + w = -1.527525232 + -1 w = -1.527525232 + -1 Combine like terms: -1.527525232 + -1 = -2.527525232 w = -2.527525232 Simplifying w = -2.527525232Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.527525232, -2.527525232}
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