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Simplifying 125x4 + 216x2 + 27 = 0 Reorder the terms: 27 + 216x2 + 125x4 = 0 Solving 27 + 216x2 + 125x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 125 the coefficient of the squared term: Divide each side by '125'. 0.216 + 1.728x2 + x4 = 0 Move the constant term to the right: Add '-0.216' to each side of the equation. 0.216 + 1.728x2 + -0.216 + x4 = 0 + -0.216 Reorder the terms: 0.216 + -0.216 + 1.728x2 + x4 = 0 + -0.216 Combine like terms: 0.216 + -0.216 = 0.000 0.000 + 1.728x2 + x4 = 0 + -0.216 1.728x2 + x4 = 0 + -0.216 Combine like terms: 0 + -0.216 = -0.216 1.728x2 + x4 = -0.216 The x term is 1.728x2. Take half its coefficient (0.864). Square it (0.746496) and add it to both sides. Add '0.746496' to each side of the equation. 1.728x2 + 0.746496 + x4 = -0.216 + 0.746496 Reorder the terms: 0.746496 + 1.728x2 + x4 = -0.216 + 0.746496 Combine like terms: -0.216 + 0.746496 = 0.530496 0.746496 + 1.728x2 + x4 = 0.530496 Factor a perfect square on the left side: (x2 + 0.864)(x2 + 0.864) = 0.530496 Calculate the square root of the right side: 0.728351563 Break this problem into two subproblems by setting (x2 + 0.864) equal to 0.728351563 and -0.728351563.Subproblem 1
x2 + 0.864 = 0.728351563 Simplifying x2 + 0.864 = 0.728351563 Reorder the terms: 0.864 + x2 = 0.728351563 Solving 0.864 + x2 = 0.728351563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.864' to each side of the equation. 0.864 + -0.864 + x2 = 0.728351563 + -0.864 Combine like terms: 0.864 + -0.864 = 0.000 0.000 + x2 = 0.728351563 + -0.864 x2 = 0.728351563 + -0.864 Combine like terms: 0.728351563 + -0.864 = -0.135648437 x2 = -0.135648437 Simplifying x2 = -0.135648437 Reorder the terms: 0.135648437 + x2 = -0.135648437 + 0.135648437 Combine like terms: -0.135648437 + 0.135648437 = 0.000000000 0.135648437 + 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 + 0.864 = -0.728351563 Simplifying x2 + 0.864 = -0.728351563 Reorder the terms: 0.864 + x2 = -0.728351563 Solving 0.864 + x2 = -0.728351563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.864' to each side of the equation. 0.864 + -0.864 + x2 = -0.728351563 + -0.864 Combine like terms: 0.864 + -0.864 = 0.000 0.000 + x2 = -0.728351563 + -0.864 x2 = -0.728351563 + -0.864 Combine like terms: -0.728351563 + -0.864 = -1.592351563 x2 = -1.592351563 Simplifying x2 = -1.592351563 Reorder the terms: 1.592351563 + x2 = -1.592351563 + 1.592351563 Combine like terms: -1.592351563 + 1.592351563 = 0.000000000 1.592351563 + 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.
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