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Simplifying 3x4 + -2x2 + -24 = 0 Reorder the terms: -24 + -2x2 + 3x4 = 0 Solving -24 + -2x2 + 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'. -8 + -0.6666666667x2 + x4 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.6666666667x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + -0.6666666667x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.6666666667x2 + x4 = 0 + 8 -0.6666666667x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.6666666667x2 + x4 = 8 The x term is -0.6666666667x2. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x2 + 0.1111111112 + x4 = 8 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x2 + x4 = 8 + 0.1111111112 Combine like terms: 8 + 0.1111111112 = 8.1111111112 0.1111111112 + -0.6666666667x2 + x4 = 8.1111111112 Factor a perfect square on the left side: (x2 + -0.3333333334)(x2 + -0.3333333334) = 8.1111111112 Calculate the square root of the right side: 2.848001248 Break this problem into two subproblems by setting (x2 + -0.3333333334) equal to 2.848001248 and -2.848001248.Subproblem 1
x2 + -0.3333333334 = 2.848001248 Simplifying x2 + -0.3333333334 = 2.848001248 Reorder the terms: -0.3333333334 + x2 = 2.848001248 Solving -0.3333333334 + x2 = 2.848001248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x2 = 2.848001248 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x2 = 2.848001248 + 0.3333333334 x2 = 2.848001248 + 0.3333333334 Combine like terms: 2.848001248 + 0.3333333334 = 3.1813345814 x2 = 3.1813345814 Simplifying x2 = 3.1813345814 Take the square root of each side: x = {-1.783629609, 1.783629609}Subproblem 2
x2 + -0.3333333334 = -2.848001248 Simplifying x2 + -0.3333333334 = -2.848001248 Reorder the terms: -0.3333333334 + x2 = -2.848001248 Solving -0.3333333334 + x2 = -2.848001248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x2 = -2.848001248 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x2 = -2.848001248 + 0.3333333334 x2 = -2.848001248 + 0.3333333334 Combine like terms: -2.848001248 + 0.3333333334 = -2.5146679146 x2 = -2.5146679146 Simplifying x2 = -2.5146679146 Reorder the terms: 2.5146679146 + x2 = -2.5146679146 + 2.5146679146 Combine like terms: -2.5146679146 + 2.5146679146 = 0.0000000000 2.5146679146 + x2 = 0.0000000000 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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