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Simplifying 64x2 + -1x + -15 = 0 Reorder the terms: -15 + -1x + 64x2 = 0 Solving -15 + -1x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.234375 + -0.015625x + x2 = 0 Move the constant term to the right: Add '0.234375' to each side of the equation. -0.234375 + -0.015625x + 0.234375 + x2 = 0 + 0.234375 Reorder the terms: -0.234375 + 0.234375 + -0.015625x + x2 = 0 + 0.234375 Combine like terms: -0.234375 + 0.234375 = 0.000000 0.000000 + -0.015625x + x2 = 0 + 0.234375 -0.015625x + x2 = 0 + 0.234375 Combine like terms: 0 + 0.234375 = 0.234375 -0.015625x + x2 = 0.234375 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 = 0.234375 + 0.00006103515625 Reorder the terms: 0.00006103515625 + -0.015625x + x2 = 0.234375 + 0.00006103515625 Combine like terms: 0.234375 + 0.00006103515625 = 0.23443603515625 0.00006103515625 + -0.015625x + x2 = 0.23443603515625 Factor a perfect square on the left side: (x + -0.0078125)(x + -0.0078125) = 0.23443603515625 Calculate the square root of the right side: 0.484185951 Break this problem into two subproblems by setting (x + -0.0078125) equal to 0.484185951 and -0.484185951.Subproblem 1
x + -0.0078125 = 0.484185951 Simplifying x + -0.0078125 = 0.484185951 Reorder the terms: -0.0078125 + x = 0.484185951 Solving -0.0078125 + x = 0.484185951 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 = 0.484185951 + 0.0078125 Combine like terms: -0.0078125 + 0.0078125 = 0.0000000 0.0000000 + x = 0.484185951 + 0.0078125 x = 0.484185951 + 0.0078125 Combine like terms: 0.484185951 + 0.0078125 = 0.491998451 x = 0.491998451 Simplifying x = 0.491998451Subproblem 2
x + -0.0078125 = -0.484185951 Simplifying x + -0.0078125 = -0.484185951 Reorder the terms: -0.0078125 + x = -0.484185951 Solving -0.0078125 + x = -0.484185951 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 = -0.484185951 + 0.0078125 Combine like terms: -0.0078125 + 0.0078125 = 0.0000000 0.0000000 + x = -0.484185951 + 0.0078125 x = -0.484185951 + 0.0078125 Combine like terms: -0.484185951 + 0.0078125 = -0.476373451 x = -0.476373451 Simplifying x = -0.476373451Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.491998451, -0.476373451}
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