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Simplifying w2 + 16w + 21 = 0 Reorder the terms: 21 + 16w + w2 = 0 Solving 21 + 16w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 16w + -21 + w2 = 0 + -21 Reorder the terms: 21 + -21 + 16w + w2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 16w + w2 = 0 + -21 16w + w2 = 0 + -21 Combine like terms: 0 + -21 = -21 16w + w2 = -21 The w term is 16w. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16w + 64 + w2 = -21 + 64 Reorder the terms: 64 + 16w + w2 = -21 + 64 Combine like terms: -21 + 64 = 43 64 + 16w + w2 = 43 Factor a perfect square on the left side: (w + 8)(w + 8) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (w + 8) equal to 6.557438524 and -6.557438524.Subproblem 1
w + 8 = 6.557438524 Simplifying w + 8 = 6.557438524 Reorder the terms: 8 + w = 6.557438524 Solving 8 + w = 6.557438524 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 6.557438524 + -8 Combine like terms: 8 + -8 = 0 0 + w = 6.557438524 + -8 w = 6.557438524 + -8 Combine like terms: 6.557438524 + -8 = -1.442561476 w = -1.442561476 Simplifying w = -1.442561476Subproblem 2
w + 8 = -6.557438524 Simplifying w + 8 = -6.557438524 Reorder the terms: 8 + w = -6.557438524 Solving 8 + w = -6.557438524 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = -6.557438524 + -8 Combine like terms: 8 + -8 = 0 0 + w = -6.557438524 + -8 w = -6.557438524 + -8 Combine like terms: -6.557438524 + -8 = -14.557438524 w = -14.557438524 Simplifying w = -14.557438524Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.442561476, -14.557438524}
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