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Simplifying 4x4 + -24x2 + -36 = 0 Reorder the terms: -36 + -24x2 + 4x4 = 0 Solving -36 + -24x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -6x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -6x2 + x4)' equal to zero and attempt to solve: Simplifying -9 + -6x2 + x4 = 0 Solving -9 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + -6x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6x2 + x4 = 0 + 9 -6x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 -6x2 + x4 = 9 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = 9 + 9 Reorder the terms: 9 + -6x2 + x4 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6x2 + x4 = 18 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x2 + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
x2 + -3 = 4.242640687 Simplifying x2 + -3 = 4.242640687 Reorder the terms: -3 + x2 = 4.242640687 Solving -3 + x2 = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 4.242640687 + 3 x2 = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 x2 = 7.242640687 Simplifying x2 = 7.242640687 Take the square root of each side: x = {-2.691215466, 2.691215466}Subproblem 2
x2 + -3 = -4.242640687 Simplifying x2 + -3 = -4.242640687 Reorder the terms: -3 + x2 = -4.242640687 Solving -3 + x2 = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -4.242640687 + 3 x2 = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 x2 = -1.242640687 Simplifying x2 = -1.242640687 Reorder the terms: 1.242640687 + x2 = -1.242640687 + 1.242640687 Combine like terms: -1.242640687 + 1.242640687 = 0.000000000 1.242640687 + 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. 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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