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Simplifying 2x4 + -73x2 + 144 = 0 Reorder the terms: 144 + -73x2 + 2x4 = 0 Solving 144 + -73x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 72 + -36.5x2 + x4 = 0 Move the constant term to the right: Add '-72' to each side of the equation. 72 + -36.5x2 + -72 + x4 = 0 + -72 Reorder the terms: 72 + -72 + -36.5x2 + x4 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -36.5x2 + x4 = 0 + -72 -36.5x2 + x4 = 0 + -72 Combine like terms: 0 + -72 = -72 -36.5x2 + x4 = -72 The x term is -36.5x2. Take half its coefficient (-18.25). Square it (333.0625) and add it to both sides. Add '333.0625' to each side of the equation. -36.5x2 + 333.0625 + x4 = -72 + 333.0625 Reorder the terms: 333.0625 + -36.5x2 + x4 = -72 + 333.0625 Combine like terms: -72 + 333.0625 = 261.0625 333.0625 + -36.5x2 + x4 = 261.0625 Factor a perfect square on the left side: (x2 + -18.25)(x2 + -18.25) = 261.0625 Calculate the square root of the right side: 16.157428632 Break this problem into two subproblems by setting (x2 + -18.25) equal to 16.157428632 and -16.157428632.Subproblem 1
x2 + -18.25 = 16.157428632 Simplifying x2 + -18.25 = 16.157428632 Reorder the terms: -18.25 + x2 = 16.157428632 Solving -18.25 + x2 = 16.157428632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.25' to each side of the equation. -18.25 + 18.25 + x2 = 16.157428632 + 18.25 Combine like terms: -18.25 + 18.25 = 0.00 0.00 + x2 = 16.157428632 + 18.25 x2 = 16.157428632 + 18.25 Combine like terms: 16.157428632 + 18.25 = 34.407428632 x2 = 34.407428632 Simplifying x2 = 34.407428632 Take the square root of each side: x = {-5.865784571, 5.865784571}Subproblem 2
x2 + -18.25 = -16.157428632 Simplifying x2 + -18.25 = -16.157428632 Reorder the terms: -18.25 + x2 = -16.157428632 Solving -18.25 + x2 = -16.157428632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.25' to each side of the equation. -18.25 + 18.25 + x2 = -16.157428632 + 18.25 Combine like terms: -18.25 + 18.25 = 0.00 0.00 + x2 = -16.157428632 + 18.25 x2 = -16.157428632 + 18.25 Combine like terms: -16.157428632 + 18.25 = 2.092571368 x2 = 2.092571368 Simplifying x2 = 2.092571368 Take the square root of each side: x = {-1.446572282, 1.446572282}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.865784571, 5.865784571, -1.446572282, 1.446572282}
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