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Simplifying 4w2 + 5w + -3 = 0 Reorder the terms: -3 + 5w + 4w2 = 0 Solving -3 + 5w + 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 + 1.25w + w2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.25w + 0.75 + w2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.25w + w2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.25w + w2 = 0 + 0.75 1.25w + w2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.25w + w2 = 0.75 The w term is 1.25w. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25w + 0.390625 + w2 = 0.75 + 0.390625 Reorder the terms: 0.390625 + 1.25w + w2 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + 1.25w + w2 = 1.140625 Factor a perfect square on the left side: (w + 0.625)(w + 0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (w + 0.625) equal to 1.068000468 and -1.068000468.Subproblem 1
w + 0.625 = 1.068000468 Simplifying w + 0.625 = 1.068000468 Reorder the terms: 0.625 + w = 1.068000468 Solving 0.625 + w = 1.068000468 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + w = 1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + w = 1.068000468 + -0.625 w = 1.068000468 + -0.625 Combine like terms: 1.068000468 + -0.625 = 0.443000468 w = 0.443000468 Simplifying w = 0.443000468Subproblem 2
w + 0.625 = -1.068000468 Simplifying w + 0.625 = -1.068000468 Reorder the terms: 0.625 + w = -1.068000468 Solving 0.625 + w = -1.068000468 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + w = -1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + w = -1.068000468 + -0.625 w = -1.068000468 + -0.625 Combine like terms: -1.068000468 + -0.625 = -1.693000468 w = -1.693000468 Simplifying w = -1.693000468Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.443000468, -1.693000468}
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