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Simplifying 5w2 + -14w + 3 = 0 Reorder the terms: 3 + -14w + 5w2 = 0 Solving 3 + -14w + 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'. 0.6 + -2.8w + w2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.8w + -0.6 + w2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.8w + w2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.8w + w2 = 0 + -0.6 -2.8w + w2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.8w + w2 = -0.6 The w term is -2.8w. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8w + 1.96 + w2 = -0.6 + 1.96 Reorder the terms: 1.96 + -2.8w + w2 = -0.6 + 1.96 Combine like terms: -0.6 + 1.96 = 1.36 1.96 + -2.8w + w2 = 1.36 Factor a perfect square on the left side: (w + -1.4)(w + -1.4) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (w + -1.4) equal to 1.166190379 and -1.166190379.Subproblem 1
w + -1.4 = 1.166190379 Simplifying w + -1.4 = 1.166190379 Reorder the terms: -1.4 + w = 1.166190379 Solving -1.4 + w = 1.166190379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + w = 1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + w = 1.166190379 + 1.4 w = 1.166190379 + 1.4 Combine like terms: 1.166190379 + 1.4 = 2.566190379 w = 2.566190379 Simplifying w = 2.566190379Subproblem 2
w + -1.4 = -1.166190379 Simplifying w + -1.4 = -1.166190379 Reorder the terms: -1.4 + w = -1.166190379 Solving -1.4 + w = -1.166190379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + w = -1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + w = -1.166190379 + 1.4 w = -1.166190379 + 1.4 Combine like terms: -1.166190379 + 1.4 = 0.233809621 w = 0.233809621 Simplifying w = 0.233809621Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.566190379, 0.233809621}
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