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Simplifying 4w2 + -9w + -3 = 0 Reorder the terms: -3 + -9w + 4w2 = 0 Solving -3 + -9w + 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'. -0.75 + -2.25w + w2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2.25w + 0.75 + w2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2.25w + w2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2.25w + w2 = 0 + 0.75 -2.25w + w2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2.25w + w2 = 0.75 The w term is -2.25w. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25w + 1.265625 + w2 = 0.75 + 1.265625 Reorder the terms: 1.265625 + -2.25w + w2 = 0.75 + 1.265625 Combine like terms: 0.75 + 1.265625 = 2.015625 1.265625 + -2.25w + w2 = 2.015625 Factor a perfect square on the left side: (w + -1.125)(w + -1.125) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (w + -1.125) equal to 1.419727086 and -1.419727086.Subproblem 1
w + -1.125 = 1.419727086 Simplifying w + -1.125 = 1.419727086 Reorder the terms: -1.125 + w = 1.419727086 Solving -1.125 + w = 1.419727086 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + w = 1.419727086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + w = 1.419727086 + 1.125 w = 1.419727086 + 1.125 Combine like terms: 1.419727086 + 1.125 = 2.544727086 w = 2.544727086 Simplifying w = 2.544727086Subproblem 2
w + -1.125 = -1.419727086 Simplifying w + -1.125 = -1.419727086 Reorder the terms: -1.125 + w = -1.419727086 Solving -1.125 + w = -1.419727086 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + w = -1.419727086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + w = -1.419727086 + 1.125 w = -1.419727086 + 1.125 Combine like terms: -1.419727086 + 1.125 = -0.294727086 w = -0.294727086 Simplifying w = -0.294727086Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.544727086, -0.294727086}
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