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Simplifying 4x2 + 64x + 64 = x + 8 Reorder the terms: 64 + 64x + 4x2 = x + 8 Reorder the terms: 64 + 64x + 4x2 = 8 + x Solving 64 + 64x + 4x2 = 8 + x Solving for variable 'x'. Reorder the terms: 64 + -8 + 64x + -1x + 4x2 = 8 + x + -8 + -1x Combine like terms: 64 + -8 = 56 56 + 64x + -1x + 4x2 = 8 + x + -8 + -1x Combine like terms: 64x + -1x = 63x 56 + 63x + 4x2 = 8 + x + -8 + -1x Reorder the terms: 56 + 63x + 4x2 = 8 + -8 + x + -1x Combine like terms: 8 + -8 = 0 56 + 63x + 4x2 = 0 + x + -1x 56 + 63x + 4x2 = x + -1x Combine like terms: x + -1x = 0 56 + 63x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 14 + 15.75x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 15.75x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 15.75x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 15.75x + x2 = 0 + -14 15.75x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 15.75x + x2 = -14 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 = -14 + 62.015625 Reorder the terms: 62.015625 + 15.75x + x2 = -14 + 62.015625 Combine like terms: -14 + 62.015625 = 48.015625 62.015625 + 15.75x + x2 = 48.015625 Factor a perfect square on the left side: (x + 7.875)(x + 7.875) = 48.015625 Calculate the square root of the right side: 6.929330776 Break this problem into two subproblems by setting (x + 7.875) equal to 6.929330776 and -6.929330776.Subproblem 1
x + 7.875 = 6.929330776 Simplifying x + 7.875 = 6.929330776 Reorder the terms: 7.875 + x = 6.929330776 Solving 7.875 + x = 6.929330776 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 = 6.929330776 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = 6.929330776 + -7.875 x = 6.929330776 + -7.875 Combine like terms: 6.929330776 + -7.875 = -0.945669224 x = -0.945669224 Simplifying x = -0.945669224Subproblem 2
x + 7.875 = -6.929330776 Simplifying x + 7.875 = -6.929330776 Reorder the terms: 7.875 + x = -6.929330776 Solving 7.875 + x = -6.929330776 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 = -6.929330776 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = -6.929330776 + -7.875 x = -6.929330776 + -7.875 Combine like terms: -6.929330776 + -7.875 = -14.804330776 x = -14.804330776 Simplifying x = -14.804330776Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.945669224, -14.804330776}
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