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Simplifying 96x4 + 144x2 + 51 = 0 Reorder the terms: 51 + 144x2 + 96x4 = 0 Solving 51 + 144x2 + 96x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(17 + 48x2 + 32x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(17 + 48x2 + 32x4)' equal to zero and attempt to solve: Simplifying 17 + 48x2 + 32x4 = 0 Solving 17 + 48x2 + 32x4 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.53125 + 1.5x2 + x4 = 0 Move the constant term to the right: Add '-0.53125' to each side of the equation. 0.53125 + 1.5x2 + -0.53125 + x4 = 0 + -0.53125 Reorder the terms: 0.53125 + -0.53125 + 1.5x2 + x4 = 0 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + 1.5x2 + x4 = 0 + -0.53125 1.5x2 + x4 = 0 + -0.53125 Combine like terms: 0 + -0.53125 = -0.53125 1.5x2 + x4 = -0.53125 The x term is 1.5x2. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x2 + 0.5625 + x4 = -0.53125 + 0.5625 Reorder the terms: 0.5625 + 1.5x2 + x4 = -0.53125 + 0.5625 Combine like terms: -0.53125 + 0.5625 = 0.03125 0.5625 + 1.5x2 + x4 = 0.03125 Factor a perfect square on the left side: (x2 + 0.75)(x2 + 0.75) = 0.03125 Calculate the square root of the right side: 0.176776695 Break this problem into two subproblems by setting (x2 + 0.75) equal to 0.176776695 and -0.176776695.Subproblem 1
x2 + 0.75 = 0.176776695 Simplifying x2 + 0.75 = 0.176776695 Reorder the terms: 0.75 + x2 = 0.176776695 Solving 0.75 + x2 = 0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = 0.176776695 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = 0.176776695 + -0.75 x2 = 0.176776695 + -0.75 Combine like terms: 0.176776695 + -0.75 = -0.573223305 x2 = -0.573223305 Simplifying x2 = -0.573223305 Reorder the terms: 0.573223305 + x2 = -0.573223305 + 0.573223305 Combine like terms: -0.573223305 + 0.573223305 = 0.000000000 0.573223305 + 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 + 0.75 = -0.176776695 Simplifying x2 + 0.75 = -0.176776695 Reorder the terms: 0.75 + x2 = -0.176776695 Solving 0.75 + x2 = -0.176776695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = -0.176776695 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = -0.176776695 + -0.75 x2 = -0.176776695 + -0.75 Combine like terms: -0.176776695 + -0.75 = -0.926776695 x2 = -0.926776695 Simplifying x2 = -0.926776695 Reorder the terms: 0.926776695 + x2 = -0.926776695 + 0.926776695 Combine like terms: -0.926776695 + 0.926776695 = 0.000000000 0.926776695 + 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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