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Simplifying 64x2 + -1x = 96 Reorder the terms: -1x + 64x2 = 96 Solving -1x + 64x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + -1x + 64x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + -1x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -1.5 + -0.015625x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.015625x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.015625x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.015625x + x2 = 0 + 1.5 -0.015625x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.015625x + x2 = 1.5 The x term is -0.015625x. Take half its coefficient (-0.0078125). Square it (0.00006103515625) and add it to both sides. Add '0.00006103515625' to each side of the equation. -0.015625x + 0.00006103515625 + x2 = 1.5 + 0.00006103515625 Reorder the terms: 0.00006103515625 + -0.015625x + x2 = 1.5 + 0.00006103515625 Combine like terms: 1.5 + 0.00006103515625 = 1.50006103515625 0.00006103515625 + -0.015625x + x2 = 1.50006103515625 Factor a perfect square on the left side: (x + -0.0078125)(x + -0.0078125) = 1.50006103515625 Calculate the square root of the right side: 1.224769789 Break this problem into two subproblems by setting (x + -0.0078125) equal to 1.224769789 and -1.224769789.Subproblem 1
x + -0.0078125 = 1.224769789 Simplifying x + -0.0078125 = 1.224769789 Reorder the terms: -0.0078125 + x = 1.224769789 Solving -0.0078125 + x = 1.224769789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0078125' to each side of the equation. -0.0078125 + 0.0078125 + x = 1.224769789 + 0.0078125 Combine like terms: -0.0078125 + 0.0078125 = 0.0000000 0.0000000 + x = 1.224769789 + 0.0078125 x = 1.224769789 + 0.0078125 Combine like terms: 1.224769789 + 0.0078125 = 1.232582289 x = 1.232582289 Simplifying x = 1.232582289Subproblem 2
x + -0.0078125 = -1.224769789 Simplifying x + -0.0078125 = -1.224769789 Reorder the terms: -0.0078125 + x = -1.224769789 Solving -0.0078125 + x = -1.224769789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0078125' to each side of the equation. -0.0078125 + 0.0078125 + x = -1.224769789 + 0.0078125 Combine like terms: -0.0078125 + 0.0078125 = 0.0000000 0.0000000 + x = -1.224769789 + 0.0078125 x = -1.224769789 + 0.0078125 Combine like terms: -1.224769789 + 0.0078125 = -1.216957289 x = -1.216957289 Simplifying x = -1.216957289Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.232582289, -1.216957289}
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