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Simplifying 4w2 + -13w + -27 = 0 Reorder the terms: -27 + -13w + 4w2 = 0 Solving -27 + -13w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + -3.25w + w2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -3.25w + 6.75 + w2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -3.25w + w2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -3.25w + w2 = 0 + 6.75 -3.25w + w2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -3.25w + w2 = 6.75 The w term is -3.25w. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25w + 2.640625 + w2 = 6.75 + 2.640625 Reorder the terms: 2.640625 + -3.25w + w2 = 6.75 + 2.640625 Combine like terms: 6.75 + 2.640625 = 9.390625 2.640625 + -3.25w + w2 = 9.390625 Factor a perfect square on the left side: (w + -1.625)(w + -1.625) = 9.390625 Calculate the square root of the right side: 3.064412668 Break this problem into two subproblems by setting (w + -1.625) equal to 3.064412668 and -3.064412668.Subproblem 1
w + -1.625 = 3.064412668 Simplifying w + -1.625 = 3.064412668 Reorder the terms: -1.625 + w = 3.064412668 Solving -1.625 + w = 3.064412668 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + w = 3.064412668 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + w = 3.064412668 + 1.625 w = 3.064412668 + 1.625 Combine like terms: 3.064412668 + 1.625 = 4.689412668 w = 4.689412668 Simplifying w = 4.689412668Subproblem 2
w + -1.625 = -3.064412668 Simplifying w + -1.625 = -3.064412668 Reorder the terms: -1.625 + w = -3.064412668 Solving -1.625 + w = -3.064412668 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + w = -3.064412668 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + w = -3.064412668 + 1.625 w = -3.064412668 + 1.625 Combine like terms: -3.064412668 + 1.625 = -1.439412668 w = -1.439412668 Simplifying w = -1.439412668Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.689412668, -1.439412668}
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