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Simplifying x4 + -72x2 + 144 = 0 Reorder the terms: 144 + -72x2 + x4 = 0 Solving 144 + -72x2 + 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 + -72x2 + -144 + x4 = 0 + -144 Reorder the terms: 144 + -144 + -72x2 + x4 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -72x2 + x4 = 0 + -144 -72x2 + x4 = 0 + -144 Combine like terms: 0 + -144 = -144 -72x2 + x4 = -144 The x term is -72x2. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x2 + 1296 + x4 = -144 + 1296 Reorder the terms: 1296 + -72x2 + x4 = -144 + 1296 Combine like terms: -144 + 1296 = 1152 1296 + -72x2 + x4 = 1152 Factor a perfect square on the left side: (x2 + -36)(x2 + -36) = 1152 Calculate the square root of the right side: 33.941125497 Break this problem into two subproblems by setting (x2 + -36) equal to 33.941125497 and -33.941125497.Subproblem 1
x2 + -36 = 33.941125497 Simplifying x2 + -36 = 33.941125497 Reorder the terms: -36 + x2 = 33.941125497 Solving -36 + x2 = 33.941125497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x2 = 33.941125497 + 36 Combine like terms: -36 + 36 = 0 0 + x2 = 33.941125497 + 36 x2 = 33.941125497 + 36 Combine like terms: 33.941125497 + 36 = 69.941125497 x2 = 69.941125497 Simplifying x2 = 69.941125497 Take the square root of each side: x = {-8.363081101, 8.363081101}Subproblem 2
x2 + -36 = -33.941125497 Simplifying x2 + -36 = -33.941125497 Reorder the terms: -36 + x2 = -33.941125497 Solving -36 + x2 = -33.941125497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x2 = -33.941125497 + 36 Combine like terms: -36 + 36 = 0 0 + x2 = -33.941125497 + 36 x2 = -33.941125497 + 36 Combine like terms: -33.941125497 + 36 = 2.058874503 x2 = 2.058874503 Simplifying x2 = 2.058874503 Take the square root of each side: x = {-1.43487787, 1.43487787}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.363081101, 8.363081101, -1.43487787, 1.43487787}
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