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Simplifying 4x4 + -24x2 + 4 = 0 Reorder the terms: 4 + -24x2 + 4x4 = 0 Solving 4 + -24x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -6x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -6x2 + x4)' equal to zero and attempt to solve: Simplifying 1 + -6x2 + x4 = 0 Solving 1 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -6x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x2 + x4 = 0 + -1 -6x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -6x2 + x4 = -1 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 = -1 + 9 Reorder the terms: 9 + -6x2 + x4 = -1 + 9 Combine like terms: -1 + 9 = 8 9 + -6x2 + x4 = 8 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x2 + -3) equal to 2.828427125 and -2.828427125.Subproblem 1
x2 + -3 = 2.828427125 Simplifying x2 + -3 = 2.828427125 Reorder the terms: -3 + x2 = 2.828427125 Solving -3 + x2 = 2.828427125 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 = 2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 2.828427125 + 3 x2 = 2.828427125 + 3 Combine like terms: 2.828427125 + 3 = 5.828427125 x2 = 5.828427125 Simplifying x2 = 5.828427125 Take the square root of each side: x = {-2.414213562, 2.414213562}Subproblem 2
x2 + -3 = -2.828427125 Simplifying x2 + -3 = -2.828427125 Reorder the terms: -3 + x2 = -2.828427125 Solving -3 + x2 = -2.828427125 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 = -2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -2.828427125 + 3 x2 = -2.828427125 + 3 Combine like terms: -2.828427125 + 3 = 0.171572875 x2 = 0.171572875 Simplifying x2 = 0.171572875 Take the square root of each side: x = {-0.414213562, 0.414213562}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.414213562, 2.414213562, -0.414213562, 0.414213562}Solution
x = {-2.414213562, 2.414213562, -0.414213562, 0.414213562}
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