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Simplifying x4 + -37x2 = -96 Reorder the terms: -37x2 + x4 = -96 Solving -37x2 + x4 = -96 Solving for variable 'x'. Reorder the terms: 96 + -37x2 + x4 = -96 + 96 Combine like terms: -96 + 96 = 0 96 + -37x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -37x2 + -96 + x4 = 0 + -96 Reorder the terms: 96 + -96 + -37x2 + x4 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -37x2 + x4 = 0 + -96 -37x2 + x4 = 0 + -96 Combine like terms: 0 + -96 = -96 -37x2 + x4 = -96 The x term is -37x2. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x2 + 342.25 + x4 = -96 + 342.25 Reorder the terms: 342.25 + -37x2 + x4 = -96 + 342.25 Combine like terms: -96 + 342.25 = 246.25 342.25 + -37x2 + x4 = 246.25 Factor a perfect square on the left side: (x2 + -18.5)(x2 + -18.5) = 246.25 Calculate the square root of the right side: 15.692354826 Break this problem into two subproblems by setting (x2 + -18.5) equal to 15.692354826 and -15.692354826.Subproblem 1
x2 + -18.5 = 15.692354826 Simplifying x2 + -18.5 = 15.692354826 Reorder the terms: -18.5 + x2 = 15.692354826 Solving -18.5 + x2 = 15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x2 = 15.692354826 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x2 = 15.692354826 + 18.5 x2 = 15.692354826 + 18.5 Combine like terms: 15.692354826 + 18.5 = 34.192354826 x2 = 34.192354826 Simplifying x2 = 34.192354826 Take the square root of each side: x = {-5.847422922, 5.847422922}Subproblem 2
x2 + -18.5 = -15.692354826 Simplifying x2 + -18.5 = -15.692354826 Reorder the terms: -18.5 + x2 = -15.692354826 Solving -18.5 + x2 = -15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x2 = -15.692354826 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x2 = -15.692354826 + 18.5 x2 = -15.692354826 + 18.5 Combine like terms: -15.692354826 + 18.5 = 2.807645174 x2 = 2.807645174 Simplifying x2 = 2.807645174 Take the square root of each side: x = {-1.675602929, 1.675602929}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.847422922, 5.847422922, -1.675602929, 1.675602929}
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