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Simplifying x4 + -9x2 + 2 = 0 Reorder the terms: 2 + -9x2 + x4 = 0 Solving 2 + -9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -9x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + -9x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9x2 + x4 = 0 + -2 -9x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 -9x2 + x4 = -2 The x term is -9x2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x2 + 20.25 + x4 = -2 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = -2 + 20.25 Combine like terms: -2 + 20.25 = 18.25 20.25 + -9x2 + x4 = 18.25 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x2 + -4.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x2 + -4.5 = 4.272001873 Simplifying x2 + -4.5 = 4.272001873 Reorder the terms: -4.5 + x2 = 4.272001873 Solving -4.5 + x2 = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 4.272001873 + 4.5 x2 = 4.272001873 + 4.5 Combine like terms: 4.272001873 + 4.5 = 8.772001873 x2 = 8.772001873 Simplifying x2 = 8.772001873 Take the square root of each side: x = {-2.961756552, 2.961756552}Subproblem 2
x2 + -4.5 = -4.272001873 Simplifying x2 + -4.5 = -4.272001873 Reorder the terms: -4.5 + x2 = -4.272001873 Solving -4.5 + x2 = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -4.272001873 + 4.5 x2 = -4.272001873 + 4.5 Combine like terms: -4.272001873 + 4.5 = 0.227998127 x2 = 0.227998127 Simplifying x2 = 0.227998127 Take the square root of each side: x = {-0.477491494, 0.477491494}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.961756552, 2.961756552, -0.477491494, 0.477491494}
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