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Simplifying 16x4 + 36x2 + -12 = 0 Reorder the terms: -12 + 36x2 + 16x4 = 0 Solving -12 + 36x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 9x2 + 4x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 9x2 + 4x4)' equal to zero and attempt to solve: Simplifying -3 + 9x2 + 4x4 = 0 Solving -3 + 9x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 2.25x2 + x4 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 2.25x2 + 0.75 + x4 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 2.25x2 + x4 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 2.25x2 + x4 = 0 + 0.75 2.25x2 + x4 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 2.25x2 + x4 = 0.75 The x term is 2.25x2. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x2 + 1.265625 + x4 = 0.75 + 1.265625 Reorder the terms: 1.265625 + 2.25x2 + x4 = 0.75 + 1.265625 Combine like terms: 0.75 + 1.265625 = 2.015625 1.265625 + 2.25x2 + x4 = 2.015625 Factor a perfect square on the left side: (x2 + 1.125)(x2 + 1.125) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x2 + 1.125) equal to 1.419727086 and -1.419727086.Subproblem 1
x2 + 1.125 = 1.419727086 Simplifying x2 + 1.125 = 1.419727086 Reorder the terms: 1.125 + x2 = 1.419727086 Solving 1.125 + x2 = 1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x2 = 1.419727086 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x2 = 1.419727086 + -1.125 x2 = 1.419727086 + -1.125 Combine like terms: 1.419727086 + -1.125 = 0.294727086 x2 = 0.294727086 Simplifying x2 = 0.294727086 Take the square root of each side: x = {-0.542887729, 0.542887729}Subproblem 2
x2 + 1.125 = -1.419727086 Simplifying x2 + 1.125 = -1.419727086 Reorder the terms: 1.125 + x2 = -1.419727086 Solving 1.125 + x2 = -1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x2 = -1.419727086 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x2 = -1.419727086 + -1.125 x2 = -1.419727086 + -1.125 Combine like terms: -1.419727086 + -1.125 = -2.544727086 x2 = -2.544727086 Simplifying x2 = -2.544727086 Reorder the terms: 2.544727086 + x2 = -2.544727086 + 2.544727086 Combine like terms: -2.544727086 + 2.544727086 = 0.000000000 2.544727086 + 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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