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Simplifying 3w2 + 9w + -221 = 0 Reorder the terms: -221 + 9w + 3w2 = 0 Solving -221 + 9w + 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'. -73.66666667 + 3w + w2 = 0 Move the constant term to the right: Add '73.66666667' to each side of the equation. -73.66666667 + 3w + 73.66666667 + w2 = 0 + 73.66666667 Reorder the terms: -73.66666667 + 73.66666667 + 3w + w2 = 0 + 73.66666667 Combine like terms: -73.66666667 + 73.66666667 = 0.00000000 0.00000000 + 3w + w2 = 0 + 73.66666667 3w + w2 = 0 + 73.66666667 Combine like terms: 0 + 73.66666667 = 73.66666667 3w + w2 = 73.66666667 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 73.66666667 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 73.66666667 + 2.25 Combine like terms: 73.66666667 + 2.25 = 75.91666667 2.25 + 3w + w2 = 75.91666667 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 75.91666667 Calculate the square root of the right side: 8.713017082 Break this problem into two subproblems by setting (w + 1.5) equal to 8.713017082 and -8.713017082.Subproblem 1
w + 1.5 = 8.713017082 Simplifying w + 1.5 = 8.713017082 Reorder the terms: 1.5 + w = 8.713017082 Solving 1.5 + w = 8.713017082 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 8.713017082 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 8.713017082 + -1.5 w = 8.713017082 + -1.5 Combine like terms: 8.713017082 + -1.5 = 7.213017082 w = 7.213017082 Simplifying w = 7.213017082Subproblem 2
w + 1.5 = -8.713017082 Simplifying w + 1.5 = -8.713017082 Reorder the terms: 1.5 + w = -8.713017082 Solving 1.5 + w = -8.713017082 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -8.713017082 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -8.713017082 + -1.5 w = -8.713017082 + -1.5 Combine like terms: -8.713017082 + -1.5 = -10.213017082 w = -10.213017082 Simplifying w = -10.213017082Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.213017082, -10.213017082}
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