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Simplifying 4w2 + 8w + -3 = 0 Reorder the terms: -3 + 8w + 4w2 = 0 Solving -3 + 8w + 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 + 2w + w2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 2w + 0.75 + w2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 2w + w2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 2w + w2 = 0 + 0.75 2w + w2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 2w + w2 = 0.75 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 0.75 + 1 Reorder the terms: 1 + 2w + w2 = 0.75 + 1 Combine like terms: 0.75 + 1 = 1.75 1 + 2w + w2 = 1.75 Factor a perfect square on the left side: (w + 1)(w + 1) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (w + 1) equal to 1.322875656 and -1.322875656.Subproblem 1
w + 1 = 1.322875656 Simplifying w + 1 = 1.322875656 Reorder the terms: 1 + w = 1.322875656 Solving 1 + w = 1.322875656 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 1.322875656 + -1 Combine like terms: 1 + -1 = 0 0 + w = 1.322875656 + -1 w = 1.322875656 + -1 Combine like terms: 1.322875656 + -1 = 0.322875656 w = 0.322875656 Simplifying w = 0.322875656Subproblem 2
w + 1 = -1.322875656 Simplifying w + 1 = -1.322875656 Reorder the terms: 1 + w = -1.322875656 Solving 1 + w = -1.322875656 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -1.322875656 + -1 Combine like terms: 1 + -1 = 0 0 + w = -1.322875656 + -1 w = -1.322875656 + -1 Combine like terms: -1.322875656 + -1 = -2.322875656 w = -2.322875656 Simplifying w = -2.322875656Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.322875656, -2.322875656}
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