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Simplifying 16x4 + -41x2 = 25 Reorder the terms: -41x2 + 16x4 = 25 Solving -41x2 + 16x4 = 25 Solving for variable 'x'. Reorder the terms: -25 + -41x2 + 16x4 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -41x2 + 16x4 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + -2.5625x2 + x4 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -2.5625x2 + 1.5625 + x4 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -2.5625x2 + x4 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -2.5625x2 + x4 = 0 + 1.5625 -2.5625x2 + x4 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -2.5625x2 + x4 = 1.5625 The x term is -2.5625x2. Take half its coefficient (-1.28125). Square it (1.641601563) and add it to both sides. Add '1.641601563' to each side of the equation. -2.5625x2 + 1.641601563 + x4 = 1.5625 + 1.641601563 Reorder the terms: 1.641601563 + -2.5625x2 + x4 = 1.5625 + 1.641601563 Combine like terms: 1.5625 + 1.641601563 = 3.204101563 1.641601563 + -2.5625x2 + x4 = 3.204101563 Factor a perfect square on the left side: (x2 + -1.28125)(x2 + -1.28125) = 3.204101563 Calculate the square root of the right side: 1.790000437 Break this problem into two subproblems by setting (x2 + -1.28125) equal to 1.790000437 and -1.790000437.Subproblem 1
x2 + -1.28125 = 1.790000437 Simplifying x2 + -1.28125 = 1.790000437 Reorder the terms: -1.28125 + x2 = 1.790000437 Solving -1.28125 + x2 = 1.790000437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.28125' to each side of the equation. -1.28125 + 1.28125 + x2 = 1.790000437 + 1.28125 Combine like terms: -1.28125 + 1.28125 = 0.00000 0.00000 + x2 = 1.790000437 + 1.28125 x2 = 1.790000437 + 1.28125 Combine like terms: 1.790000437 + 1.28125 = 3.071250437 x2 = 3.071250437 Simplifying x2 = 3.071250437 Take the square root of each side: x = {-1.752498342, 1.752498342}Subproblem 2
x2 + -1.28125 = -1.790000437 Simplifying x2 + -1.28125 = -1.790000437 Reorder the terms: -1.28125 + x2 = -1.790000437 Solving -1.28125 + x2 = -1.790000437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.28125' to each side of the equation. -1.28125 + 1.28125 + x2 = -1.790000437 + 1.28125 Combine like terms: -1.28125 + 1.28125 = 0.00000 0.00000 + x2 = -1.790000437 + 1.28125 x2 = -1.790000437 + 1.28125 Combine like terms: -1.790000437 + 1.28125 = -0.508750437 x2 = -0.508750437 Simplifying x2 = -0.508750437 Reorder the terms: 0.508750437 + x2 = -0.508750437 + 0.508750437 Combine like terms: -0.508750437 + 0.508750437 = 0.000000000 0.508750437 + x2 = 0.000000000 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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