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Simplifying 6x4 + -9x2 = 3 Reorder the terms: -9x2 + 6x4 = 3 Solving -9x2 + 6x4 = 3 Solving for variable 'x'. Reorder the terms: -3 + -9x2 + 6x4 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -9x2 + 6x4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -3x2 + 2x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -3x2 + 2x4)' equal to zero and attempt to solve: Simplifying -1 + -3x2 + 2x4 = 0 Solving -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 = 1.780776406 x2 = 1.780776406 Simplifying x2 = 1.780776406 Take the square root of each side: x = {-1.334457345, 1.334457345}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 = -0.280776406 x2 = -0.280776406 Simplifying x2 = -0.280776406 Reorder the terms: 0.280776406 + x2 = -0.280776406 + 0.280776406 Combine like terms: -0.280776406 + 0.280776406 = 0.000000000 0.280776406 + 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. 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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