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Simplifying 18x4 + -22x2 + -324 = 0 Reorder the terms: -324 + -22x2 + 18x4 = 0 Solving -324 + -22x2 + 18x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-162 + -11x2 + 9x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-162 + -11x2 + 9x4)' equal to zero and attempt to solve: Simplifying -162 + -11x2 + 9x4 = 0 Solving -162 + -11x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -18 + -1.222222222x2 + x4 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -1.222222222x2 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + -1.222222222x2 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1.222222222x2 + x4 = 0 + 18 -1.222222222x2 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 -1.222222222x2 + x4 = 18 The x term is -1.222222222x2. Take half its coefficient (-0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. -1.222222222x2 + 0.3734567900 + x4 = 18 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222x2 + x4 = 18 + 0.3734567900 Combine like terms: 18 + 0.3734567900 = 18.37345679 0.3734567900 + -1.222222222x2 + x4 = 18.37345679 Factor a perfect square on the left side: (x2 + -0.611111111)(x2 + -0.611111111) = 18.37345679 Calculate the square root of the right side: 4.286427042 Break this problem into two subproblems by setting (x2 + -0.611111111) equal to 4.286427042 and -4.286427042.Subproblem 1
x2 + -0.611111111 = 4.286427042 Simplifying x2 + -0.611111111 = 4.286427042 Reorder the terms: -0.611111111 + x2 = 4.286427042 Solving -0.611111111 + x2 = 4.286427042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x2 = 4.286427042 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x2 = 4.286427042 + 0.611111111 x2 = 4.286427042 + 0.611111111 Combine like terms: 4.286427042 + 0.611111111 = 4.897538153 x2 = 4.897538153 Simplifying x2 = 4.897538153 Take the square root of each side: x = {-2.213038218, 2.213038218}Subproblem 2
x2 + -0.611111111 = -4.286427042 Simplifying x2 + -0.611111111 = -4.286427042 Reorder the terms: -0.611111111 + x2 = -4.286427042 Solving -0.611111111 + x2 = -4.286427042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x2 = -4.286427042 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x2 = -4.286427042 + 0.611111111 x2 = -4.286427042 + 0.611111111 Combine like terms: -4.286427042 + 0.611111111 = -3.675315931 x2 = -3.675315931 Simplifying x2 = -3.675315931 Reorder the terms: 3.675315931 + x2 = -3.675315931 + 3.675315931 Combine like terms: -3.675315931 + 3.675315931 = 0.000000000 3.675315931 + 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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