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Simplifying 12w2 + -10w = (2w) * 3w + 5 Reorder the terms: -10w + 12w2 = (2w) * 3w + 5 Remove parenthesis around (2w) -10w + 12w2 = 2w * 3w + 5 Reorder the terms for easier multiplication: -10w + 12w2 = 2 * 3w * w + 5 Multiply 2 * 3 -10w + 12w2 = 6w * w + 5 Multiply w * w -10w + 12w2 = 6w2 + 5 Reorder the terms: -10w + 12w2 = 5 + 6w2 Solving -10w + 12w2 = 5 + 6w2 Solving for variable 'w'. Reorder the terms: -5 + -10w + 12w2 + -6w2 = 5 + 6w2 + -5 + -6w2 Combine like terms: 12w2 + -6w2 = 6w2 -5 + -10w + 6w2 = 5 + 6w2 + -5 + -6w2 Reorder the terms: -5 + -10w + 6w2 = 5 + -5 + 6w2 + -6w2 Combine like terms: 5 + -5 = 0 -5 + -10w + 6w2 = 0 + 6w2 + -6w2 -5 + -10w + 6w2 = 6w2 + -6w2 Combine like terms: 6w2 + -6w2 = 0 -5 + -10w + 6w2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -1.666666667w + w2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -1.666666667w + 0.8333333333 + w2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -1.666666667w + w2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -1.666666667w + w2 = 0 + 0.8333333333 -1.666666667w + w2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -1.666666667w + w2 = 0.8333333333 The w term is -1.666666667w. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667w + 0.6944444447 + w2 = 0.8333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667w + w2 = 0.8333333333 + 0.6944444447 Combine like terms: 0.8333333333 + 0.6944444447 = 1.527777778 0.6944444447 + -1.666666667w + w2 = 1.527777778 Factor a perfect square on the left side: (w + -0.8333333335)(w + -0.8333333335) = 1.527777778 Calculate the square root of the right side: 1.236033081 Break this problem into two subproblems by setting (w + -0.8333333335) equal to 1.236033081 and -1.236033081.Subproblem 1
w + -0.8333333335 = 1.236033081 Simplifying w + -0.8333333335 = 1.236033081 Reorder the terms: -0.8333333335 + w = 1.236033081 Solving -0.8333333335 + w = 1.236033081 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = 1.236033081 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = 1.236033081 + 0.8333333335 w = 1.236033081 + 0.8333333335 Combine like terms: 1.236033081 + 0.8333333335 = 2.0693664145 w = 2.0693664145 Simplifying w = 2.0693664145Subproblem 2
w + -0.8333333335 = -1.236033081 Simplifying w + -0.8333333335 = -1.236033081 Reorder the terms: -0.8333333335 + w = -1.236033081 Solving -0.8333333335 + w = -1.236033081 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = -1.236033081 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = -1.236033081 + 0.8333333335 w = -1.236033081 + 0.8333333335 Combine like terms: -1.236033081 + 0.8333333335 = -0.4026997475 w = -0.4026997475 Simplifying w = -0.4026997475Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.0693664145, -0.4026997475}
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