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Simplifying 5w + 5w + w2 = 84 Combine like terms: 5w + 5w = 10w 10w + w2 = 84 Solving 10w + w2 = 84 Solving for variable 'w'. Reorder the terms: -84 + 10w + w2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 10w + 84 + w2 = 0 + 84 Reorder the terms: -84 + 84 + 10w + w2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 10w + w2 = 0 + 84 10w + w2 = 0 + 84 Combine like terms: 0 + 84 = 84 10w + w2 = 84 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 = 84 + 25 Reorder the terms: 25 + 10w + w2 = 84 + 25 Combine like terms: 84 + 25 = 109 25 + 10w + w2 = 109 Factor a perfect square on the left side: (w + 5)(w + 5) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (w + 5) equal to 10.440306509 and -10.440306509.Subproblem 1
w + 5 = 10.440306509 Simplifying w + 5 = 10.440306509 Reorder the terms: 5 + w = 10.440306509 Solving 5 + w = 10.440306509 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 = 10.440306509 + -5 Combine like terms: 5 + -5 = 0 0 + w = 10.440306509 + -5 w = 10.440306509 + -5 Combine like terms: 10.440306509 + -5 = 5.440306509 w = 5.440306509 Simplifying w = 5.440306509Subproblem 2
w + 5 = -10.440306509 Simplifying w + 5 = -10.440306509 Reorder the terms: 5 + w = -10.440306509 Solving 5 + w = -10.440306509 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 = -10.440306509 + -5 Combine like terms: 5 + -5 = 0 0 + w = -10.440306509 + -5 w = -10.440306509 + -5 Combine like terms: -10.440306509 + -5 = -15.440306509 w = -15.440306509 Simplifying w = -15.440306509Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.440306509, -15.440306509}
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