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Simplifying 5(w * w) + -3w + -17 = 0 Multiply w * w 5(w2) + -3w + -17 = 0 Reorder the terms: -17 + -3w + 5w2 = 0 Solving -17 + -3w + 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'. -3.4 + -0.6w + w2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -0.6w + 3.4 + w2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -0.6w + w2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -0.6w + w2 = 0 + 3.4 -0.6w + w2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -0.6w + w2 = 3.4 The w term is -0.6w. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6w + 0.09 + w2 = 3.4 + 0.09 Reorder the terms: 0.09 + -0.6w + w2 = 3.4 + 0.09 Combine like terms: 3.4 + 0.09 = 3.49 0.09 + -0.6w + w2 = 3.49 Factor a perfect square on the left side: (w + -0.3)(w + -0.3) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (w + -0.3) equal to 1.868154169 and -1.868154169.Subproblem 1
w + -0.3 = 1.868154169 Simplifying w + -0.3 = 1.868154169 Reorder the terms: -0.3 + w = 1.868154169 Solving -0.3 + w = 1.868154169 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + w = 1.868154169 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = 1.868154169 + 0.3 w = 1.868154169 + 0.3 Combine like terms: 1.868154169 + 0.3 = 2.168154169 w = 2.168154169 Simplifying w = 2.168154169Subproblem 2
w + -0.3 = -1.868154169 Simplifying w + -0.3 = -1.868154169 Reorder the terms: -0.3 + w = -1.868154169 Solving -0.3 + w = -1.868154169 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + w = -1.868154169 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = -1.868154169 + 0.3 w = -1.868154169 + 0.3 Combine like terms: -1.868154169 + 0.3 = -1.568154169 w = -1.568154169 Simplifying w = -1.568154169Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.168154169, -1.568154169}
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