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Simplifying 5w2 + 44w + -63 = 0 Reorder the terms: -63 + 44w + 5w2 = 0 Solving -63 + 44w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + 8.8w + w2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + 8.8w + 12.6 + w2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + 8.8w + w2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + 8.8w + w2 = 0 + 12.6 8.8w + w2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 8.8w + w2 = 12.6 The w term is 8.8w. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8w + 19.36 + w2 = 12.6 + 19.36 Reorder the terms: 19.36 + 8.8w + w2 = 12.6 + 19.36 Combine like terms: 12.6 + 19.36 = 31.96 19.36 + 8.8w + w2 = 31.96 Factor a perfect square on the left side: (w + 4.4)(w + 4.4) = 31.96 Calculate the square root of the right side: 5.65331761 Break this problem into two subproblems by setting (w + 4.4) equal to 5.65331761 and -5.65331761.Subproblem 1
w + 4.4 = 5.65331761 Simplifying w + 4.4 = 5.65331761 Reorder the terms: 4.4 + w = 5.65331761 Solving 4.4 + w = 5.65331761 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + w = 5.65331761 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + w = 5.65331761 + -4.4 w = 5.65331761 + -4.4 Combine like terms: 5.65331761 + -4.4 = 1.25331761 w = 1.25331761 Simplifying w = 1.25331761Subproblem 2
w + 4.4 = -5.65331761 Simplifying w + 4.4 = -5.65331761 Reorder the terms: 4.4 + w = -5.65331761 Solving 4.4 + w = -5.65331761 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + w = -5.65331761 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + w = -5.65331761 + -4.4 w = -5.65331761 + -4.4 Combine like terms: -5.65331761 + -4.4 = -10.05331761 w = -10.05331761 Simplifying w = -10.05331761Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.25331761, -10.05331761}
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