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Simplifying 12w2 + 19w = 4 Reorder the terms: 19w + 12w2 = 4 Solving 19w + 12w2 = 4 Solving for variable 'w'. Reorder the terms: -4 + 19w + 12w2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 19w + 12w2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + 1.583333333w + w2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.583333333w + 0.3333333333 + w2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.583333333w + w2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.583333333w + w2 = 0 + 0.3333333333 1.583333333w + w2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.583333333w + w2 = 0.3333333333 The w term is 1.583333333w. Take half its coefficient (0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. 1.583333333w + 0.6267361108 + w2 = 0.3333333333 + 0.6267361108 Reorder the terms: 0.6267361108 + 1.583333333w + w2 = 0.3333333333 + 0.6267361108 Combine like terms: 0.3333333333 + 0.6267361108 = 0.9600694441 0.6267361108 + 1.583333333w + w2 = 0.9600694441 Factor a perfect square on the left side: (w + 0.7916666665)(w + 0.7916666665) = 0.9600694441 Calculate the square root of the right side: 0.979831335 Break this problem into two subproblems by setting (w + 0.7916666665) equal to 0.979831335 and -0.979831335.Subproblem 1
w + 0.7916666665 = 0.979831335 Simplifying w + 0.7916666665 = 0.979831335 Reorder the terms: 0.7916666665 + w = 0.979831335 Solving 0.7916666665 + w = 0.979831335 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + w = 0.979831335 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + w = 0.979831335 + -0.7916666665 w = 0.979831335 + -0.7916666665 Combine like terms: 0.979831335 + -0.7916666665 = 0.1881646685 w = 0.1881646685 Simplifying w = 0.1881646685Subproblem 2
w + 0.7916666665 = -0.979831335 Simplifying w + 0.7916666665 = -0.979831335 Reorder the terms: 0.7916666665 + w = -0.979831335 Solving 0.7916666665 + w = -0.979831335 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.7916666665' to each side of the equation. 0.7916666665 + -0.7916666665 + w = -0.979831335 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + w = -0.979831335 + -0.7916666665 w = -0.979831335 + -0.7916666665 Combine like terms: -0.979831335 + -0.7916666665 = -1.7714980015 w = -1.7714980015 Simplifying w = -1.7714980015Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.1881646685, -1.7714980015}
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