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Simplifying 5w2 + -3w + -6 = 0 Reorder the terms: -6 + -3w + 5w2 = 0 Solving -6 + -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'. -1.2 + -0.6w + w2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.6w + 1.2 + w2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.6w + w2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.6w + w2 = 0 + 1.2 -0.6w + w2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.6w + w2 = 1.2 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 = 1.2 + 0.09 Reorder the terms: 0.09 + -0.6w + w2 = 1.2 + 0.09 Combine like terms: 1.2 + 0.09 = 1.29 0.09 + -0.6w + w2 = 1.29 Factor a perfect square on the left side: (w + -0.3)(w + -0.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (w + -0.3) equal to 1.135781669 and -1.135781669.Subproblem 1
w + -0.3 = 1.135781669 Simplifying w + -0.3 = 1.135781669 Reorder the terms: -0.3 + w = 1.135781669 Solving -0.3 + w = 1.135781669 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 = 1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = 1.135781669 + 0.3 w = 1.135781669 + 0.3 Combine like terms: 1.135781669 + 0.3 = 1.435781669 w = 1.435781669 Simplifying w = 1.435781669Subproblem 2
w + -0.3 = -1.135781669 Simplifying w + -0.3 = -1.135781669 Reorder the terms: -0.3 + w = -1.135781669 Solving -0.3 + w = -1.135781669 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 = -1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = -1.135781669 + 0.3 w = -1.135781669 + 0.3 Combine like terms: -1.135781669 + 0.3 = -0.835781669 w = -0.835781669 Simplifying w = -0.835781669Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.435781669, -0.835781669}
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