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Simplifying 8x2 + 134x + 525 = 1050 Reorder the terms: 525 + 134x + 8x2 = 1050 Solving 525 + 134x + 8x2 = 1050 Solving for variable 'x'. Reorder the terms: 525 + -1050 + 134x + 8x2 = 1050 + -1050 Combine like terms: 525 + -1050 = -525 -525 + 134x + 8x2 = 1050 + -1050 Combine like terms: 1050 + -1050 = 0 -525 + 134x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -65.625 + 16.75x + x2 = 0 Move the constant term to the right: Add '65.625' to each side of the equation. -65.625 + 16.75x + 65.625 + x2 = 0 + 65.625 Reorder the terms: -65.625 + 65.625 + 16.75x + x2 = 0 + 65.625 Combine like terms: -65.625 + 65.625 = 0.000 0.000 + 16.75x + x2 = 0 + 65.625 16.75x + x2 = 0 + 65.625 Combine like terms: 0 + 65.625 = 65.625 16.75x + x2 = 65.625 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 = 65.625 + 70.140625 Reorder the terms: 70.140625 + 16.75x + x2 = 65.625 + 70.140625 Combine like terms: 65.625 + 70.140625 = 135.765625 70.140625 + 16.75x + x2 = 135.765625 Factor a perfect square on the left side: (x + 8.375)(x + 8.375) = 135.765625 Calculate the square root of the right side: 11.651850711 Break this problem into two subproblems by setting (x + 8.375) equal to 11.651850711 and -11.651850711.Subproblem 1
x + 8.375 = 11.651850711 Simplifying x + 8.375 = 11.651850711 Reorder the terms: 8.375 + x = 11.651850711 Solving 8.375 + x = 11.651850711 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 = 11.651850711 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = 11.651850711 + -8.375 x = 11.651850711 + -8.375 Combine like terms: 11.651850711 + -8.375 = 3.276850711 x = 3.276850711 Simplifying x = 3.276850711Subproblem 2
x + 8.375 = -11.651850711 Simplifying x + 8.375 = -11.651850711 Reorder the terms: 8.375 + x = -11.651850711 Solving 8.375 + x = -11.651850711 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 = -11.651850711 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = -11.651850711 + -8.375 x = -11.651850711 + -8.375 Combine like terms: -11.651850711 + -8.375 = -20.026850711 x = -20.026850711 Simplifying x = -20.026850711Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.276850711, -20.026850711}
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