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Simplifying w2 + 6w + -186 = 0 Reorder the terms: -186 + 6w + w2 = 0 Solving -186 + 6w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '186' to each side of the equation. -186 + 6w + 186 + w2 = 0 + 186 Reorder the terms: -186 + 186 + 6w + w2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + 6w + w2 = 0 + 186 6w + w2 = 0 + 186 Combine like terms: 0 + 186 = 186 6w + w2 = 186 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 = 186 + 9 Reorder the terms: 9 + 6w + w2 = 186 + 9 Combine like terms: 186 + 9 = 195 9 + 6w + w2 = 195 Factor a perfect square on the left side: (w + 3)(w + 3) = 195 Calculate the square root of the right side: 13.964240044 Break this problem into two subproblems by setting (w + 3) equal to 13.964240044 and -13.964240044.Subproblem 1
w + 3 = 13.964240044 Simplifying w + 3 = 13.964240044 Reorder the terms: 3 + w = 13.964240044 Solving 3 + w = 13.964240044 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 = 13.964240044 + -3 Combine like terms: 3 + -3 = 0 0 + w = 13.964240044 + -3 w = 13.964240044 + -3 Combine like terms: 13.964240044 + -3 = 10.964240044 w = 10.964240044 Simplifying w = 10.964240044Subproblem 2
w + 3 = -13.964240044 Simplifying w + 3 = -13.964240044 Reorder the terms: 3 + w = -13.964240044 Solving 3 + w = -13.964240044 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 = -13.964240044 + -3 Combine like terms: 3 + -3 = 0 0 + w = -13.964240044 + -3 w = -13.964240044 + -3 Combine like terms: -13.964240044 + -3 = -16.964240044 w = -16.964240044 Simplifying w = -16.964240044Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.964240044, -16.964240044}
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