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Simplifying x4 + -24x2 + 20 = 0 Reorder the terms: 20 + -24x2 + x4 = 0 Solving 20 + -24x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -24x2 + -20 + x4 = 0 + -20 Reorder the terms: 20 + -20 + -24x2 + x4 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -24x2 + x4 = 0 + -20 -24x2 + x4 = 0 + -20 Combine like terms: 0 + -20 = -20 -24x2 + x4 = -20 The x term is -24x2. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x2 + 144 + x4 = -20 + 144 Reorder the terms: 144 + -24x2 + x4 = -20 + 144 Combine like terms: -20 + 144 = 124 144 + -24x2 + x4 = 124 Factor a perfect square on the left side: (x2 + -12)(x2 + -12) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x2 + -12) equal to 11.135528726 and -11.135528726.Subproblem 1
x2 + -12 = 11.135528726 Simplifying x2 + -12 = 11.135528726 Reorder the terms: -12 + x2 = 11.135528726 Solving -12 + x2 = 11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x2 = 11.135528726 + 12 Combine like terms: -12 + 12 = 0 0 + x2 = 11.135528726 + 12 x2 = 11.135528726 + 12 Combine like terms: 11.135528726 + 12 = 23.135528726 x2 = 23.135528726 Simplifying x2 = 23.135528726 Take the square root of each side: x = {-4.809940616, 4.809940616}Subproblem 2
x2 + -12 = -11.135528726 Simplifying x2 + -12 = -11.135528726 Reorder the terms: -12 + x2 = -11.135528726 Solving -12 + x2 = -11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x2 = -11.135528726 + 12 Combine like terms: -12 + 12 = 0 0 + x2 = -11.135528726 + 12 x2 = -11.135528726 + 12 Combine like terms: -11.135528726 + 12 = 0.864471274 x2 = 0.864471274 Simplifying x2 = 0.864471274 Take the square root of each side: x = {-0.929769474, 0.929769474}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.809940616, 4.809940616, -0.929769474, 0.929769474}
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