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Simplifying w2 + -10w = 47 Reorder the terms: -10w + w2 = 47 Solving -10w + w2 = 47 Solving for variable 'w'. Reorder the terms: -47 + -10w + w2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -10w + 47 + w2 = 0 + 47 Reorder the terms: -47 + 47 + -10w + w2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -10w + w2 = 0 + 47 -10w + w2 = 0 + 47 Combine like terms: 0 + 47 = 47 -10w + w2 = 47 The w term is -10w. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10w + 25 + w2 = 47 + 25 Reorder the terms: 25 + -10w + w2 = 47 + 25 Combine like terms: 47 + 25 = 72 25 + -10w + w2 = 72 Factor a perfect square on the left side: (w + -5)(w + -5) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (w + -5) equal to 8.485281374 and -8.485281374.Subproblem 1
w + -5 = 8.485281374 Simplifying w + -5 = 8.485281374 Reorder the terms: -5 + w = 8.485281374 Solving -5 + w = 8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 8.485281374 + 5 Combine like terms: -5 + 5 = 0 0 + w = 8.485281374 + 5 w = 8.485281374 + 5 Combine like terms: 8.485281374 + 5 = 13.485281374 w = 13.485281374 Simplifying w = 13.485281374Subproblem 2
w + -5 = -8.485281374 Simplifying w + -5 = -8.485281374 Reorder the terms: -5 + w = -8.485281374 Solving -5 + w = -8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = -8.485281374 + 5 Combine like terms: -5 + 5 = 0 0 + w = -8.485281374 + 5 w = -8.485281374 + 5 Combine like terms: -8.485281374 + 5 = -3.485281374 w = -3.485281374 Simplifying w = -3.485281374Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.485281374, -3.485281374}
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