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Simplifying 4x4 + -3x2 + -9 = 0 Reorder the terms: -9 + -3x2 + 4x4 = 0 Solving -9 + -3x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -0.75x2 + x4 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.75x2 + 2.25 + x4 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.75x2 + x4 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.75x2 + x4 = 0 + 2.25 -0.75x2 + x4 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.75x2 + x4 = 2.25 The x term is -0.75x2. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x2 + 0.140625 + x4 = 2.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x2 + x4 = 2.25 + 0.140625 Combine like terms: 2.25 + 0.140625 = 2.390625 0.140625 + -0.75x2 + x4 = 2.390625 Factor a perfect square on the left side: (x2 + -0.375)(x2 + -0.375) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x2 + -0.375) equal to 1.54616461 and -1.54616461.Subproblem 1
x2 + -0.375 = 1.54616461 Simplifying x2 + -0.375 = 1.54616461 Reorder the terms: -0.375 + x2 = 1.54616461 Solving -0.375 + x2 = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x2 = 1.54616461 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x2 = 1.54616461 + 0.375 x2 = 1.54616461 + 0.375 Combine like terms: 1.54616461 + 0.375 = 1.92116461 x2 = 1.92116461 Simplifying x2 = 1.92116461 Take the square root of each side: x = {-1.386060825, 1.386060825}Subproblem 2
x2 + -0.375 = -1.54616461 Simplifying x2 + -0.375 = -1.54616461 Reorder the terms: -0.375 + x2 = -1.54616461 Solving -0.375 + x2 = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x2 = -1.54616461 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x2 = -1.54616461 + 0.375 x2 = -1.54616461 + 0.375 Combine like terms: -1.54616461 + 0.375 = -1.17116461 x2 = -1.17116461 Simplifying x2 = -1.17116461 Reorder the terms: 1.17116461 + x2 = -1.17116461 + 1.17116461 Combine like terms: -1.17116461 + 1.17116461 = 0.00000000 1.17116461 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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