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Simplifying 32x2 + 536x + 1575 = 0 Reorder the terms: 1575 + 536x + 32x2 = 0 Solving 1575 + 536x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 49.21875 + 16.75x + x2 = 0 Move the constant term to the right: Add '-49.21875' to each side of the equation. 49.21875 + 16.75x + -49.21875 + x2 = 0 + -49.21875 Reorder the terms: 49.21875 + -49.21875 + 16.75x + x2 = 0 + -49.21875 Combine like terms: 49.21875 + -49.21875 = 0.00000 0.00000 + 16.75x + x2 = 0 + -49.21875 16.75x + x2 = 0 + -49.21875 Combine like terms: 0 + -49.21875 = -49.21875 16.75x + x2 = -49.21875 The x term is 16.75x. Take half its coefficient (8.375). Square it (70.140625) and add it to both sides. Add '70.140625' to each side of the equation. 16.75x + 70.140625 + x2 = -49.21875 + 70.140625 Reorder the terms: 70.140625 + 16.75x + x2 = -49.21875 + 70.140625 Combine like terms: -49.21875 + 70.140625 = 20.921875 70.140625 + 16.75x + x2 = 20.921875 Factor a perfect square on the left side: (x + 8.375)(x + 8.375) = 20.921875 Calculate the square root of the right side: 4.574043616 Break this problem into two subproblems by setting (x + 8.375) equal to 4.574043616 and -4.574043616.Subproblem 1
x + 8.375 = 4.574043616 Simplifying x + 8.375 = 4.574043616 Reorder the terms: 8.375 + x = 4.574043616 Solving 8.375 + x = 4.574043616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = 4.574043616 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = 4.574043616 + -8.375 x = 4.574043616 + -8.375 Combine like terms: 4.574043616 + -8.375 = -3.800956384 x = -3.800956384 Simplifying x = -3.800956384Subproblem 2
x + 8.375 = -4.574043616 Simplifying x + 8.375 = -4.574043616 Reorder the terms: 8.375 + x = -4.574043616 Solving 8.375 + x = -4.574043616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = -4.574043616 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = -4.574043616 + -8.375 x = -4.574043616 + -8.375 Combine like terms: -4.574043616 + -8.375 = -12.949043616 x = -12.949043616 Simplifying x = -12.949043616Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.800956384, -12.949043616}
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