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Simplifying 13824000 = x + 16x * x + -1 Multiply x * x 13824000 = x + 16x2 + -1 Reorder the terms: 13824000 = -1 + x + 16x2 Solving 13824000 = -1 + x + 16x2 Solving for variable 'x'. Combine like terms: 13824000 + 1 = 13824001 13824001 + -1x + -16x2 = -1 + x + 16x2 + 1 + -1x + -16x2 Reorder the terms: 13824001 + -1x + -16x2 = -1 + 1 + x + -1x + 16x2 + -16x2 Combine like terms: -1 + 1 = 0 13824001 + -1x + -16x2 = 0 + x + -1x + 16x2 + -16x2 13824001 + -1x + -16x2 = x + -1x + 16x2 + -16x2 Combine like terms: x + -1x = 0 13824001 + -1x + -16x2 = 0 + 16x2 + -16x2 13824001 + -1x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 13824001 + -1x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -864000.0625 + 0.0625x + x2 = 0 Move the constant term to the right: Add '864000.0625' to each side of the equation. -864000.0625 + 0.0625x + 864000.0625 + x2 = 0 + 864000.0625 Reorder the terms: -864000.0625 + 864000.0625 + 0.0625x + x2 = 0 + 864000.0625 Combine like terms: -864000.0625 + 864000.0625 = 0.0000 0.0000 + 0.0625x + x2 = 0 + 864000.0625 0.0625x + x2 = 0 + 864000.0625 Combine like terms: 0 + 864000.0625 = 864000.0625 0.0625x + x2 = 864000.0625 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 864000.0625 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 864000.0625 + 0.0009765625 Combine like terms: 864000.0625 + 0.0009765625 = 864000.0634765625 0.0009765625 + 0.0625x + x2 = 864000.0634765625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 864000.0634765625 Calculate the square root of the right side: 929.516037235 Break this problem into two subproblems by setting (x + 0.03125) equal to 929.516037235 and -929.516037235.Subproblem 1
x + 0.03125 = 929.516037235 Simplifying x + 0.03125 = 929.516037235 Reorder the terms: 0.03125 + x = 929.516037235 Solving 0.03125 + x = 929.516037235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 929.516037235 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 929.516037235 + -0.03125 x = 929.516037235 + -0.03125 Combine like terms: 929.516037235 + -0.03125 = 929.484787235 x = 929.484787235 Simplifying x = 929.484787235Subproblem 2
x + 0.03125 = -929.516037235 Simplifying x + 0.03125 = -929.516037235 Reorder the terms: 0.03125 + x = -929.516037235 Solving 0.03125 + x = -929.516037235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -929.516037235 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -929.516037235 + -0.03125 x = -929.516037235 + -0.03125 Combine like terms: -929.516037235 + -0.03125 = -929.547287235 x = -929.547287235 Simplifying x = -929.547287235Solution
The solution to the problem is based on the solutions from the subproblems. x = {929.484787235, -929.547287235}
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