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Simplifying -5w2 + -13w + 16 = 0 Reorder the terms: 16 + -13w + -5w2 = 0 Solving 16 + -13w + -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'. -3.2 + 2.6w + w2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 2.6w + 3.2 + w2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 2.6w + w2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 2.6w + w2 = 0 + 3.2 2.6w + w2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 2.6w + w2 = 3.2 The w term is 2.6w. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6w + 1.69 + w2 = 3.2 + 1.69 Reorder the terms: 1.69 + 2.6w + w2 = 3.2 + 1.69 Combine like terms: 3.2 + 1.69 = 4.89 1.69 + 2.6w + w2 = 4.89 Factor a perfect square on the left side: (w + 1.3)(w + 1.3) = 4.89 Calculate the square root of the right side: 2.211334439 Break this problem into two subproblems by setting (w + 1.3) equal to 2.211334439 and -2.211334439.Subproblem 1
w + 1.3 = 2.211334439 Simplifying w + 1.3 = 2.211334439 Reorder the terms: 1.3 + w = 2.211334439 Solving 1.3 + w = 2.211334439 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + w = 2.211334439 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + w = 2.211334439 + -1.3 w = 2.211334439 + -1.3 Combine like terms: 2.211334439 + -1.3 = 0.911334439 w = 0.911334439 Simplifying w = 0.911334439Subproblem 2
w + 1.3 = -2.211334439 Simplifying w + 1.3 = -2.211334439 Reorder the terms: 1.3 + w = -2.211334439 Solving 1.3 + w = -2.211334439 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + w = -2.211334439 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + w = -2.211334439 + -1.3 w = -2.211334439 + -1.3 Combine like terms: -2.211334439 + -1.3 = -3.511334439 w = -3.511334439 Simplifying w = -3.511334439Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.911334439, -3.511334439}
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