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Simplifying -2w2 + 7w + 19 = 0 Reorder the terms: 19 + 7w + -2w2 = 0 Solving 19 + 7w + -2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -9.5 + -3.5w + w2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -3.5w + 9.5 + w2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -3.5w + w2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -3.5w + w2 = 0 + 9.5 -3.5w + w2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -3.5w + w2 = 9.5 The w term is -3.5w. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5w + 3.0625 + w2 = 9.5 + 3.0625 Reorder the terms: 3.0625 + -3.5w + w2 = 9.5 + 3.0625 Combine like terms: 9.5 + 3.0625 = 12.5625 3.0625 + -3.5w + w2 = 12.5625 Factor a perfect square on the left side: (w + -1.75)(w + -1.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (w + -1.75) equal to 3.54436172 and -3.54436172.Subproblem 1
w + -1.75 = 3.54436172 Simplifying w + -1.75 = 3.54436172 Reorder the terms: -1.75 + w = 3.54436172 Solving -1.75 + w = 3.54436172 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = 3.54436172 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = 3.54436172 + 1.75 w = 3.54436172 + 1.75 Combine like terms: 3.54436172 + 1.75 = 5.29436172 w = 5.29436172 Simplifying w = 5.29436172Subproblem 2
w + -1.75 = -3.54436172 Simplifying w + -1.75 = -3.54436172 Reorder the terms: -1.75 + w = -3.54436172 Solving -1.75 + w = -3.54436172 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = -3.54436172 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = -3.54436172 + 1.75 w = -3.54436172 + 1.75 Combine like terms: -3.54436172 + 1.75 = -1.79436172 w = -1.79436172 Simplifying w = -1.79436172Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.29436172, -1.79436172}
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