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Simplifying w + 9 = w2 + 3w + -4 Reorder the terms: 9 + w = w2 + 3w + -4 Reorder the terms: 9 + w = -4 + 3w + w2 Solving 9 + w = -4 + 3w + w2 Solving for variable 'w'. Reorder the terms: 9 + 4 + w + -3w + -1w2 = -4 + 3w + w2 + 4 + -3w + -1w2 Combine like terms: 9 + 4 = 13 13 + w + -3w + -1w2 = -4 + 3w + w2 + 4 + -3w + -1w2 Combine like terms: w + -3w = -2w 13 + -2w + -1w2 = -4 + 3w + w2 + 4 + -3w + -1w2 Reorder the terms: 13 + -2w + -1w2 = -4 + 4 + 3w + -3w + w2 + -1w2 Combine like terms: -4 + 4 = 0 13 + -2w + -1w2 = 0 + 3w + -3w + w2 + -1w2 13 + -2w + -1w2 = 3w + -3w + w2 + -1w2 Combine like terms: 3w + -3w = 0 13 + -2w + -1w2 = 0 + w2 + -1w2 13 + -2w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 13 + -2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 2w + w2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 2w + 13 + w2 = 0 + 13 Reorder the terms: -13 + 13 + 2w + w2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2w + w2 = 0 + 13 2w + w2 = 0 + 13 Combine like terms: 0 + 13 = 13 2w + w2 = 13 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 = 13 + 1 Reorder the terms: 1 + 2w + w2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2w + w2 = 14 Factor a perfect square on the left side: (w + 1)(w + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (w + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
w + 1 = 3.741657387 Simplifying w + 1 = 3.741657387 Reorder the terms: 1 + w = 3.741657387 Solving 1 + w = 3.741657387 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 = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + w = 3.741657387 + -1 w = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 w = 2.741657387 Simplifying w = 2.741657387Subproblem 2
w + 1 = -3.741657387 Simplifying w + 1 = -3.741657387 Reorder the terms: 1 + w = -3.741657387 Solving 1 + w = -3.741657387 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 = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + w = -3.741657387 + -1 w = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 w = -4.741657387 Simplifying w = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.741657387, -4.741657387}
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