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Simplifying 0 = w2 + 2w + -84 Reorder the terms: 0 = -84 + 2w + w2 Solving 0 = -84 + 2w + w2 Solving for variable 'w'. Combine like terms: 0 + 84 = 84 84 + -2w + -1w2 = -84 + 2w + w2 + 84 + -2w + -1w2 Reorder the terms: 84 + -2w + -1w2 = -84 + 84 + 2w + -2w + w2 + -1w2 Combine like terms: -84 + 84 = 0 84 + -2w + -1w2 = 0 + 2w + -2w + w2 + -1w2 84 + -2w + -1w2 = 2w + -2w + w2 + -1w2 Combine like terms: 2w + -2w = 0 84 + -2w + -1w2 = 0 + w2 + -1w2 84 + -2w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 84 + -2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -84 + 2w + w2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + 2w + 84 + w2 = 0 + 84 Reorder the terms: -84 + 84 + 2w + w2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 2w + w2 = 0 + 84 2w + w2 = 0 + 84 Combine like terms: 0 + 84 = 84 2w + w2 = 84 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 = 84 + 1 Reorder the terms: 1 + 2w + w2 = 84 + 1 Combine like terms: 84 + 1 = 85 1 + 2w + w2 = 85 Factor a perfect square on the left side: (w + 1)(w + 1) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (w + 1) equal to 9.219544457 and -9.219544457.Subproblem 1
w + 1 = 9.219544457 Simplifying w + 1 = 9.219544457 Reorder the terms: 1 + w = 9.219544457 Solving 1 + w = 9.219544457 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 = 9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + w = 9.219544457 + -1 w = 9.219544457 + -1 Combine like terms: 9.219544457 + -1 = 8.219544457 w = 8.219544457 Simplifying w = 8.219544457Subproblem 2
w + 1 = -9.219544457 Simplifying w + 1 = -9.219544457 Reorder the terms: 1 + w = -9.219544457 Solving 1 + w = -9.219544457 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 = -9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + w = -9.219544457 + -1 w = -9.219544457 + -1 Combine like terms: -9.219544457 + -1 = -10.219544457 w = -10.219544457 Simplifying w = -10.219544457Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.219544457, -10.219544457}
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