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Simplifying (4(x4)) + (64(x2)) + -225 = 0 Reorder the terms: -225 + (64x2) + (4x4) = 0 Solving -225 + (64x2) + (4x4) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -56.25 + (16x2) + x4 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + (16x2) + 56.25 + x4 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + (16x2) + x4 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + (16x2) + x4 = 0 + 56.25 (16x2) + x4 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 (16x2) + x4 = 56.25 The x term is (16x2). Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. (16x2) + 64 + x4 = 56.25 + 64 Reorder the terms: 64 + (16x2) + x4 = 56.25 + 64 Combine like terms: 56.25 + 64 = 120.25 64 + (16x2) + x4 = 120.25 Factor a perfect square on the left side: ((x2) + 8)((x2) + 8) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting ((x2) + 8) equal to 10.9658561 and -10.9658561.Subproblem 1
(x2) + 8 = 10.9658561 Simplifying (x2) + 8 = 10.9658561 x2 + 8 = 10.9658561 Reorder the terms: 8 + x2 = 10.9658561 Solving 8 + x2 = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = 10.9658561 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 10.9658561 + -8 x2 = 10.9658561 + -8 Combine like terms: 10.9658561 + -8 = 2.9658561 x2 = 2.9658561 Simplifying x2 = 2.9658561 Take the square root of each side: x = {-1.722166107, 1.722166107}Subproblem 2
(x2) + 8 = -10.9658561 Simplifying (x2) + 8 = -10.9658561 x2 + 8 = -10.9658561 Reorder the terms: 8 + x2 = -10.9658561 Solving 8 + x2 = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = -10.9658561 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -10.9658561 + -8 x2 = -10.9658561 + -8 Combine like terms: -10.9658561 + -8 = -18.9658561 x2 = -18.9658561 Simplifying x2 = -18.9658561 Reorder the terms: 18.9658561 + x2 = -18.9658561 + 18.9658561 Combine like terms: -18.9658561 + 18.9658561 = 0.0000000 18.9658561 + x2 = 0.0000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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