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Simplifying 4x4 = 24x2 + 8 Reorder the terms: 4x4 = 8 + 24x2 Solving 4x4 = 8 + 24x2 Solving for variable 'x'. Reorder the terms: -8 + -24x2 + 4x4 = 8 + 24x2 + -8 + -24x2 Reorder the terms: -8 + -24x2 + 4x4 = 8 + -8 + 24x2 + -24x2 Combine like terms: 8 + -8 = 0 -8 + -24x2 + 4x4 = 0 + 24x2 + -24x2 -8 + -24x2 + 4x4 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -8 + -24x2 + 4x4 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -6x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -6x2 + x4)' equal to zero and attempt to solve: Simplifying -2 + -6x2 + x4 = 0 Solving -2 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -6x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + -6x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6x2 + x4 = 0 + 2 -6x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 -6x2 + x4 = 2 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 = 2 + 9 Reorder the terms: 9 + -6x2 + x4 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + -6x2 + x4 = 11 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x2 + -3) equal to 3.31662479 and -3.31662479.Subproblem 1
x2 + -3 = 3.31662479 Simplifying x2 + -3 = 3.31662479 Reorder the terms: -3 + x2 = 3.31662479 Solving -3 + x2 = 3.31662479 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 = 3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 3.31662479 + 3 x2 = 3.31662479 + 3 Combine like terms: 3.31662479 + 3 = 6.31662479 x2 = 6.31662479 Simplifying x2 = 6.31662479 Take the square root of each side: x = {-2.513289635, 2.513289635}Subproblem 2
x2 + -3 = -3.31662479 Simplifying x2 + -3 = -3.31662479 Reorder the terms: -3 + x2 = -3.31662479 Solving -3 + x2 = -3.31662479 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 = -3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -3.31662479 + 3 x2 = -3.31662479 + 3 Combine like terms: -3.31662479 + 3 = -0.31662479 x2 = -0.31662479 Simplifying x2 = -0.31662479 Reorder the terms: 0.31662479 + x2 = -0.31662479 + 0.31662479 Combine like terms: -0.31662479 + 0.31662479 = 0.00000000 0.31662479 + x2 = 0.00000000 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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