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Simplifying 3x4 + 32x2 + -192 = 0 Reorder the terms: -192 + 32x2 + 3x4 = 0 Solving -192 + 32x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -64 + 10.66666667x2 + x4 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 10.66666667x2 + 64 + x4 = 0 + 64 Reorder the terms: -64 + 64 + 10.66666667x2 + x4 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 10.66666667x2 + x4 = 0 + 64 10.66666667x2 + x4 = 0 + 64 Combine like terms: 0 + 64 = 64 10.66666667x2 + x4 = 64 The x term is 10.66666667x2. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x2 + 28.44444446 + x4 = 64 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x2 + x4 = 64 + 28.44444446 Combine like terms: 64 + 28.44444446 = 92.44444446 28.44444446 + 10.66666667x2 + x4 = 92.44444446 Factor a perfect square on the left side: (x2 + 5.333333335)(x2 + 5.333333335) = 92.44444446 Calculate the square root of the right side: 9.614803402 Break this problem into two subproblems by setting (x2 + 5.333333335) equal to 9.614803402 and -9.614803402.Subproblem 1
x2 + 5.333333335 = 9.614803402 Simplifying x2 + 5.333333335 = 9.614803402 Reorder the terms: 5.333333335 + x2 = 9.614803402 Solving 5.333333335 + x2 = 9.614803402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x2 = 9.614803402 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x2 = 9.614803402 + -5.333333335 x2 = 9.614803402 + -5.333333335 Combine like terms: 9.614803402 + -5.333333335 = 4.281470067 x2 = 4.281470067 Simplifying x2 = 4.281470067 Take the square root of each side: x = {-2.069171348, 2.069171348}Subproblem 2
x2 + 5.333333335 = -9.614803402 Simplifying x2 + 5.333333335 = -9.614803402 Reorder the terms: 5.333333335 + x2 = -9.614803402 Solving 5.333333335 + x2 = -9.614803402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x2 = -9.614803402 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x2 = -9.614803402 + -5.333333335 x2 = -9.614803402 + -5.333333335 Combine like terms: -9.614803402 + -5.333333335 = -14.948136737 x2 = -14.948136737 Simplifying x2 = -14.948136737 Reorder the terms: 14.948136737 + x2 = -14.948136737 + 14.948136737 Combine like terms: -14.948136737 + 14.948136737 = 0.000000000 14.948136737 + x2 = 0.000000000 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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