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Simplifying 0 = 8x2 + 126x + -35 Reorder the terms: 0 = -35 + 126x + 8x2 Solving 0 = -35 + 126x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 35 = 35 35 + -126x + -8x2 = -35 + 126x + 8x2 + 35 + -126x + -8x2 Reorder the terms: 35 + -126x + -8x2 = -35 + 35 + 126x + -126x + 8x2 + -8x2 Combine like terms: -35 + 35 = 0 35 + -126x + -8x2 = 0 + 126x + -126x + 8x2 + -8x2 35 + -126x + -8x2 = 126x + -126x + 8x2 + -8x2 Combine like terms: 126x + -126x = 0 35 + -126x + -8x2 = 0 + 8x2 + -8x2 35 + -126x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 35 + -126x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.375 + 15.75x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 15.75x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 15.75x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 15.75x + x2 = 0 + 4.375 15.75x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 15.75x + x2 = 4.375 The x term is 15.75x. Take half its coefficient (7.875). Square it (62.015625) and add it to both sides. Add '62.015625' to each side of the equation. 15.75x + 62.015625 + x2 = 4.375 + 62.015625 Reorder the terms: 62.015625 + 15.75x + x2 = 4.375 + 62.015625 Combine like terms: 4.375 + 62.015625 = 66.390625 62.015625 + 15.75x + x2 = 66.390625 Factor a perfect square on the left side: (x + 7.875)(x + 7.875) = 66.390625 Calculate the square root of the right side: 8.148044244 Break this problem into two subproblems by setting (x + 7.875) equal to 8.148044244 and -8.148044244.Subproblem 1
x + 7.875 = 8.148044244 Simplifying x + 7.875 = 8.148044244 Reorder the terms: 7.875 + x = 8.148044244 Solving 7.875 + x = 8.148044244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + x = 8.148044244 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = 8.148044244 + -7.875 x = 8.148044244 + -7.875 Combine like terms: 8.148044244 + -7.875 = 0.273044244 x = 0.273044244 Simplifying x = 0.273044244Subproblem 2
x + 7.875 = -8.148044244 Simplifying x + 7.875 = -8.148044244 Reorder the terms: 7.875 + x = -8.148044244 Solving 7.875 + x = -8.148044244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + x = -8.148044244 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = -8.148044244 + -7.875 x = -8.148044244 + -7.875 Combine like terms: -8.148044244 + -7.875 = -16.023044244 x = -16.023044244 Simplifying x = -16.023044244Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.273044244, -16.023044244}
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