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Simplifying 2x4 + 3x2 = 1 Reorder the terms: 3x2 + 2x4 = 1 Solving 3x2 + 2x4 = 1 Solving for variable 'x'. Reorder the terms: -1 + 3x2 + 2x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 3x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 1.5x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.5x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.5x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.5x2 + x4 = 0 + 0.5 1.5x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.5x2 + x4 = 0.5 The x term is 1.5x2. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x2 + 0.5625 + x4 = 0.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x2 + x4 = 0.5 + 0.5625 Combine like terms: 0.5 + 0.5625 = 1.0625 0.5625 + 1.5x2 + x4 = 1.0625 Factor a perfect square on the left side: (x2 + 0.75)(x2 + 0.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x2 + 0.75) equal to 1.030776406 and -1.030776406.Subproblem 1
x2 + 0.75 = 1.030776406 Simplifying x2 + 0.75 = 1.030776406 Reorder the terms: 0.75 + x2 = 1.030776406 Solving 0.75 + x2 = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = 1.030776406 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = 1.030776406 + -0.75 x2 = 1.030776406 + -0.75 Combine like terms: 1.030776406 + -0.75 = 0.280776406 x2 = 0.280776406 Simplifying x2 = 0.280776406 Take the square root of each side: x = {-0.529883389, 0.529883389}Subproblem 2
x2 + 0.75 = -1.030776406 Simplifying x2 + 0.75 = -1.030776406 Reorder the terms: 0.75 + x2 = -1.030776406 Solving 0.75 + x2 = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = -1.030776406 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = -1.030776406 + -0.75 x2 = -1.030776406 + -0.75 Combine like terms: -1.030776406 + -0.75 = -1.780776406 x2 = -1.780776406 Simplifying x2 = -1.780776406 Reorder the terms: 1.780776406 + x2 = -1.780776406 + 1.780776406 Combine like terms: -1.780776406 + 1.780776406 = 0.000000000 1.780776406 + 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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