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Simplifying w2 = -42 + -35w Solving w2 = -42 + -35w Solving for variable 'w'. Reorder the terms: 42 + 35w + w2 = -42 + -35w + 42 + 35w Reorder the terms: 42 + 35w + w2 = -42 + 42 + -35w + 35w Combine like terms: -42 + 42 = 0 42 + 35w + w2 = 0 + -35w + 35w 42 + 35w + w2 = -35w + 35w Combine like terms: -35w + 35w = 0 42 + 35w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 35w + -42 + w2 = 0 + -42 Reorder the terms: 42 + -42 + 35w + w2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 35w + w2 = 0 + -42 35w + w2 = 0 + -42 Combine like terms: 0 + -42 = -42 35w + w2 = -42 The w term is 35w. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35w + 306.25 + w2 = -42 + 306.25 Reorder the terms: 306.25 + 35w + w2 = -42 + 306.25 Combine like terms: -42 + 306.25 = 264.25 306.25 + 35w + w2 = 264.25 Factor a perfect square on the left side: (w + 17.5)(w + 17.5) = 264.25 Calculate the square root of the right side: 16.255768207 Break this problem into two subproblems by setting (w + 17.5) equal to 16.255768207 and -16.255768207.Subproblem 1
w + 17.5 = 16.255768207 Simplifying w + 17.5 = 16.255768207 Reorder the terms: 17.5 + w = 16.255768207 Solving 17.5 + w = 16.255768207 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + w = 16.255768207 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + w = 16.255768207 + -17.5 w = 16.255768207 + -17.5 Combine like terms: 16.255768207 + -17.5 = -1.244231793 w = -1.244231793 Simplifying w = -1.244231793Subproblem 2
w + 17.5 = -16.255768207 Simplifying w + 17.5 = -16.255768207 Reorder the terms: 17.5 + w = -16.255768207 Solving 17.5 + w = -16.255768207 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + w = -16.255768207 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + w = -16.255768207 + -17.5 w = -16.255768207 + -17.5 Combine like terms: -16.255768207 + -17.5 = -33.755768207 w = -33.755768207 Simplifying w = -33.755768207Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.244231793, -33.755768207}
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