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Simplifying x2 + -5x2 + -2x4 + 24 = 0 Reorder the terms: 24 + x2 + -5x2 + -2x4 = 0 Combine like terms: x2 + -5x2 = -4x2 24 + -4x2 + -2x4 = 0 Solving 24 + -4x2 + -2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -2x2 + -1x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -2x2 + -1x4)' equal to zero and attempt to solve: Simplifying 12 + -2x2 + -1x4 = 0 Solving 12 + -2x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 2x2 + x4 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 2x2 + 12 + x4 = 0 + 12 Reorder the terms: -12 + 12 + 2x2 + x4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2x2 + x4 = 0 + 12 2x2 + x4 = 0 + 12 Combine like terms: 0 + 12 = 12 2x2 + x4 = 12 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 12 + 1 Reorder the terms: 1 + 2x2 + x4 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + 2x2 + x4 = 13 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x2 + 1) equal to 3.605551275 and -3.605551275.Subproblem 1
x2 + 1 = 3.605551275 Simplifying x2 + 1 = 3.605551275 Reorder the terms: 1 + x2 = 3.605551275 Solving 1 + x2 = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 3.605551275 + -1 x2 = 3.605551275 + -1 Combine like terms: 3.605551275 + -1 = 2.605551275 x2 = 2.605551275 Simplifying x2 = 2.605551275 Take the square root of each side: x = {-1.614172009, 1.614172009}Subproblem 2
x2 + 1 = -3.605551275 Simplifying x2 + 1 = -3.605551275 Reorder the terms: 1 + x2 = -3.605551275 Solving 1 + x2 = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -3.605551275 + -1 x2 = -3.605551275 + -1 Combine like terms: -3.605551275 + -1 = -4.605551275 x2 = -4.605551275 Simplifying x2 = -4.605551275 Reorder the terms: 4.605551275 + x2 = -4.605551275 + 4.605551275 Combine like terms: -4.605551275 + 4.605551275 = 0.000000000 4.605551275 + 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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