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Simplifying w2 + 15w + 21 = 0 Reorder the terms: 21 + 15w + w2 = 0 Solving 21 + 15w + 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 + 15w + -21 + w2 = 0 + -21 Reorder the terms: 21 + -21 + 15w + w2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 15w + w2 = 0 + -21 15w + w2 = 0 + -21 Combine like terms: 0 + -21 = -21 15w + w2 = -21 The w term is 15w. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15w + 56.25 + w2 = -21 + 56.25 Reorder the terms: 56.25 + 15w + w2 = -21 + 56.25 Combine like terms: -21 + 56.25 = 35.25 56.25 + 15w + w2 = 35.25 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (w + 7.5) equal to 5.937171044 and -5.937171044.Subproblem 1
w + 7.5 = 5.937171044 Simplifying w + 7.5 = 5.937171044 Reorder the terms: 7.5 + w = 5.937171044 Solving 7.5 + w = 5.937171044 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 5.937171044 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 5.937171044 + -7.5 w = 5.937171044 + -7.5 Combine like terms: 5.937171044 + -7.5 = -1.562828956 w = -1.562828956 Simplifying w = -1.562828956Subproblem 2
w + 7.5 = -5.937171044 Simplifying w + 7.5 = -5.937171044 Reorder the terms: 7.5 + w = -5.937171044 Solving 7.5 + w = -5.937171044 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -5.937171044 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -5.937171044 + -7.5 w = -5.937171044 + -7.5 Combine like terms: -5.937171044 + -7.5 = -13.437171044 w = -13.437171044 Simplifying w = -13.437171044Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.562828956, -13.437171044}
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