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Simplifying 20x4 + 72x2 + 16 = 0 Reorder the terms: 16 + 72x2 + 20x4 = 0 Solving 16 + 72x2 + 20x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 18x2 + 5x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + 18x2 + 5x4)' equal to zero and attempt to solve: Simplifying 4 + 18x2 + 5x4 = 0 Solving 4 + 18x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 3.6x2 + x4 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 3.6x2 + -0.8 + x4 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 3.6x2 + x4 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 3.6x2 + x4 = 0 + -0.8 3.6x2 + x4 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 3.6x2 + x4 = -0.8 The x term is 3.6x2. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x2 + 3.24 + x4 = -0.8 + 3.24 Reorder the terms: 3.24 + 3.6x2 + x4 = -0.8 + 3.24 Combine like terms: -0.8 + 3.24 = 2.44 3.24 + 3.6x2 + x4 = 2.44 Factor a perfect square on the left side: (x2 + 1.8)(x2 + 1.8) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (x2 + 1.8) equal to 1.562049935 and -1.562049935.Subproblem 1
x2 + 1.8 = 1.562049935 Simplifying x2 + 1.8 = 1.562049935 Reorder the terms: 1.8 + x2 = 1.562049935 Solving 1.8 + x2 = 1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x2 = 1.562049935 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x2 = 1.562049935 + -1.8 x2 = 1.562049935 + -1.8 Combine like terms: 1.562049935 + -1.8 = -0.237950065 x2 = -0.237950065 Simplifying x2 = -0.237950065 Reorder the terms: 0.237950065 + x2 = -0.237950065 + 0.237950065 Combine like terms: -0.237950065 + 0.237950065 = 0.000000000 0.237950065 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 1.8 = -1.562049935 Simplifying x2 + 1.8 = -1.562049935 Reorder the terms: 1.8 + x2 = -1.562049935 Solving 1.8 + x2 = -1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x2 = -1.562049935 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x2 = -1.562049935 + -1.8 x2 = -1.562049935 + -1.8 Combine like terms: -1.562049935 + -1.8 = -3.362049935 x2 = -3.362049935 Simplifying x2 = -3.362049935 Reorder the terms: 3.362049935 + x2 = -3.362049935 + 3.362049935 Combine like terms: -3.362049935 + 3.362049935 = 0.000000000 3.362049935 + 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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