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Simplifying -27x4 + -24x2 + 8 = 0 Reorder the terms: 8 + -24x2 + -27x4 = 0 Solving 8 + -24x2 + -27x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. -0.2962962963 + 0.8888888889x2 + x4 = 0 Move the constant term to the right: Add '0.2962962963' to each side of the equation. -0.2962962963 + 0.8888888889x2 + 0.2962962963 + x4 = 0 + 0.2962962963 Reorder the terms: -0.2962962963 + 0.2962962963 + 0.8888888889x2 + x4 = 0 + 0.2962962963 Combine like terms: -0.2962962963 + 0.2962962963 = 0.0000000000 0.0000000000 + 0.8888888889x2 + x4 = 0 + 0.2962962963 0.8888888889x2 + x4 = 0 + 0.2962962963 Combine like terms: 0 + 0.2962962963 = 0.2962962963 0.8888888889x2 + x4 = 0.2962962963 The x term is 0.8888888889x2. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x2 + 0.1975308642 + x4 = 0.2962962963 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x2 + x4 = 0.2962962963 + 0.1975308642 Combine like terms: 0.2962962963 + 0.1975308642 = 0.4938271605 0.1975308642 + 0.8888888889x2 + x4 = 0.4938271605 Factor a perfect square on the left side: (x2 + 0.4444444445)(x2 + 0.4444444445) = 0.4938271605 Calculate the square root of the right side: 0.702728369 Break this problem into two subproblems by setting (x2 + 0.4444444445) equal to 0.702728369 and -0.702728369.Subproblem 1
x2 + 0.4444444445 = 0.702728369 Simplifying x2 + 0.4444444445 = 0.702728369 Reorder the terms: 0.4444444445 + x2 = 0.702728369 Solving 0.4444444445 + x2 = 0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x2 = 0.702728369 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x2 = 0.702728369 + -0.4444444445 x2 = 0.702728369 + -0.4444444445 Combine like terms: 0.702728369 + -0.4444444445 = 0.2582839245 x2 = 0.2582839245 Simplifying x2 = 0.2582839245 Take the square root of each side: x = {-0.508216415, 0.508216415}Subproblem 2
x2 + 0.4444444445 = -0.702728369 Simplifying x2 + 0.4444444445 = -0.702728369 Reorder the terms: 0.4444444445 + x2 = -0.702728369 Solving 0.4444444445 + x2 = -0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x2 = -0.702728369 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x2 = -0.702728369 + -0.4444444445 x2 = -0.702728369 + -0.4444444445 Combine like terms: -0.702728369 + -0.4444444445 = -1.1471728135 x2 = -1.1471728135 Simplifying x2 = -1.1471728135 Reorder the terms: 1.1471728135 + x2 = -1.1471728135 + 1.1471728135 Combine like terms: -1.1471728135 + 1.1471728135 = 0.0000000000 1.1471728135 + x2 = 0.0000000000 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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