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Simplifying x4 + -36x2 + 144 = 0 Reorder the terms: 144 + -36x2 + x4 = 0 Solving 144 + -36x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -36x2 + -144 + x4 = 0 + -144 Reorder the terms: 144 + -144 + -36x2 + x4 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -36x2 + x4 = 0 + -144 -36x2 + x4 = 0 + -144 Combine like terms: 0 + -144 = -144 -36x2 + x4 = -144 The x term is -36x2. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x2 + 324 + x4 = -144 + 324 Reorder the terms: 324 + -36x2 + x4 = -144 + 324 Combine like terms: -144 + 324 = 180 324 + -36x2 + x4 = 180 Factor a perfect square on the left side: (x2 + -18)(x2 + -18) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x2 + -18) equal to 13.416407865 and -13.416407865.Subproblem 1
x2 + -18 = 13.416407865 Simplifying x2 + -18 = 13.416407865 Reorder the terms: -18 + x2 = 13.416407865 Solving -18 + x2 = 13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x2 = 13.416407865 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = 13.416407865 + 18 x2 = 13.416407865 + 18 Combine like terms: 13.416407865 + 18 = 31.416407865 x2 = 31.416407865 Simplifying x2 = 31.416407865 Take the square root of each side: x = {-5.605034154, 5.605034154}Subproblem 2
x2 + -18 = -13.416407865 Simplifying x2 + -18 = -13.416407865 Reorder the terms: -18 + x2 = -13.416407865 Solving -18 + x2 = -13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x2 = -13.416407865 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = -13.416407865 + 18 x2 = -13.416407865 + 18 Combine like terms: -13.416407865 + 18 = 4.583592135 x2 = 4.583592135 Simplifying x2 = 4.583592135 Take the square root of each side: x = {-2.140932539, 2.140932539}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.605034154, 5.605034154, -2.140932539, 2.140932539}
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