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Simplifying 7(w + 20) * w = 5 Reorder the terms: 7(20 + w) * w = 5 Reorder the terms for easier multiplication: 7w(20 + w) = 5 (20 * 7w + w * 7w) = 5 (140w + 7w2) = 5 Solving 140w + 7w2 = 5 Solving for variable 'w'. Reorder the terms: -5 + 140w + 7w2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 140w + 7w2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 20w + w2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 20w + 0.7142857143 + w2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 20w + w2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 20w + w2 = 0 + 0.7142857143 20w + w2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 20w + w2 = 0.7142857143 The w term is 20w. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20w + 100 + w2 = 0.7142857143 + 100 Reorder the terms: 100 + 20w + w2 = 0.7142857143 + 100 Combine like terms: 0.7142857143 + 100 = 100.7142857143 100 + 20w + w2 = 100.7142857143 Factor a perfect square on the left side: (w + 10)(w + 10) = 100.7142857143 Calculate the square root of the right side: 10.035650737 Break this problem into two subproblems by setting (w + 10) equal to 10.035650737 and -10.035650737.Subproblem 1
w + 10 = 10.035650737 Simplifying w + 10 = 10.035650737 Reorder the terms: 10 + w = 10.035650737 Solving 10 + w = 10.035650737 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 10.035650737 + -10 Combine like terms: 10 + -10 = 0 0 + w = 10.035650737 + -10 w = 10.035650737 + -10 Combine like terms: 10.035650737 + -10 = 0.035650737 w = 0.035650737 Simplifying w = 0.035650737Subproblem 2
w + 10 = -10.035650737 Simplifying w + 10 = -10.035650737 Reorder the terms: 10 + w = -10.035650737 Solving 10 + w = -10.035650737 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = -10.035650737 + -10 Combine like terms: 10 + -10 = 0 0 + w = -10.035650737 + -10 w = -10.035650737 + -10 Combine like terms: -10.035650737 + -10 = -20.035650737 w = -20.035650737 Simplifying w = -20.035650737Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.035650737, -20.035650737}
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