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Simplifying w2 + 6w + -290 = 0 Reorder the terms: -290 + 6w + w2 = 0 Solving -290 + 6w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '290' to each side of the equation. -290 + 6w + 290 + w2 = 0 + 290 Reorder the terms: -290 + 290 + 6w + w2 = 0 + 290 Combine like terms: -290 + 290 = 0 0 + 6w + w2 = 0 + 290 6w + w2 = 0 + 290 Combine like terms: 0 + 290 = 290 6w + w2 = 290 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 290 + 9 Reorder the terms: 9 + 6w + w2 = 290 + 9 Combine like terms: 290 + 9 = 299 9 + 6w + w2 = 299 Factor a perfect square on the left side: (w + 3)(w + 3) = 299 Calculate the square root of the right side: 17.291616466 Break this problem into two subproblems by setting (w + 3) equal to 17.291616466 and -17.291616466.Subproblem 1
w + 3 = 17.291616466 Simplifying w + 3 = 17.291616466 Reorder the terms: 3 + w = 17.291616466 Solving 3 + w = 17.291616466 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 17.291616466 + -3 Combine like terms: 3 + -3 = 0 0 + w = 17.291616466 + -3 w = 17.291616466 + -3 Combine like terms: 17.291616466 + -3 = 14.291616466 w = 14.291616466 Simplifying w = 14.291616466Subproblem 2
w + 3 = -17.291616466 Simplifying w + 3 = -17.291616466 Reorder the terms: 3 + w = -17.291616466 Solving 3 + w = -17.291616466 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -17.291616466 + -3 Combine like terms: 3 + -3 = 0 0 + w = -17.291616466 + -3 w = -17.291616466 + -3 Combine like terms: -17.291616466 + -3 = -20.291616466 w = -20.291616466 Simplifying w = -20.291616466Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.291616466, -20.291616466}
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