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Simplifying 6x4 + -9x2 + -64 = 0 Reorder the terms: -64 + -9x2 + 6x4 = 0 Solving -64 + -9x2 + 6x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.66666667 + -1.5x2 + x4 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -1.5x2 + 10.66666667 + x4 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -1.5x2 + x4 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -1.5x2 + x4 = 0 + 10.66666667 -1.5x2 + x4 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -1.5x2 + x4 = 10.66666667 The x term is -1.5x2. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x2 + 0.5625 + x4 = 10.66666667 + 0.5625 Reorder the terms: 0.5625 + -1.5x2 + x4 = 10.66666667 + 0.5625 Combine like terms: 10.66666667 + 0.5625 = 11.22916667 0.5625 + -1.5x2 + x4 = 11.22916667 Factor a perfect square on the left side: (x2 + -0.75)(x2 + -0.75) = 11.22916667 Calculate the square root of the right side: 3.350994878 Break this problem into two subproblems by setting (x2 + -0.75) equal to 3.350994878 and -3.350994878.Subproblem 1
x2 + -0.75 = 3.350994878 Simplifying x2 + -0.75 = 3.350994878 Reorder the terms: -0.75 + x2 = 3.350994878 Solving -0.75 + x2 = 3.350994878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x2 = 3.350994878 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x2 = 3.350994878 + 0.75 x2 = 3.350994878 + 0.75 Combine like terms: 3.350994878 + 0.75 = 4.100994878 x2 = 4.100994878 Simplifying x2 = 4.100994878 Take the square root of each side: x = {-2.025091326, 2.025091326}Subproblem 2
x2 + -0.75 = -3.350994878 Simplifying x2 + -0.75 = -3.350994878 Reorder the terms: -0.75 + x2 = -3.350994878 Solving -0.75 + x2 = -3.350994878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x2 = -3.350994878 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x2 = -3.350994878 + 0.75 x2 = -3.350994878 + 0.75 Combine like terms: -3.350994878 + 0.75 = -2.600994878 x2 = -2.600994878 Simplifying x2 = -2.600994878 Reorder the terms: 2.600994878 + x2 = -2.600994878 + 2.600994878 Combine like terms: -2.600994878 + 2.600994878 = 0.000000000 2.600994878 + 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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