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Simplifying 12x4 + 8x2 + -3 = 0 Reorder the terms: -3 + 8x2 + 12x4 = 0 Solving -3 + 8x2 + 12x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.25 + 0.6666666667x2 + x4 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.6666666667x2 + 0.25 + x4 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.6666666667x2 + x4 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.6666666667x2 + x4 = 0 + 0.25 0.6666666667x2 + x4 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.6666666667x2 + x4 = 0.25 The x term is 0.6666666667x2. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x2 + 0.1111111112 + x4 = 0.25 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x2 + x4 = 0.25 + 0.1111111112 Combine like terms: 0.25 + 0.1111111112 = 0.3611111112 0.1111111112 + 0.6666666667x2 + x4 = 0.3611111112 Factor a perfect square on the left side: (x2 + 0.3333333334)(x2 + 0.3333333334) = 0.3611111112 Calculate the square root of the right side: 0.600925213 Break this problem into two subproblems by setting (x2 + 0.3333333334) equal to 0.600925213 and -0.600925213.Subproblem 1
x2 + 0.3333333334 = 0.600925213 Simplifying x2 + 0.3333333334 = 0.600925213 Reorder the terms: 0.3333333334 + x2 = 0.600925213 Solving 0.3333333334 + x2 = 0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x2 = 0.600925213 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x2 = 0.600925213 + -0.3333333334 x2 = 0.600925213 + -0.3333333334 Combine like terms: 0.600925213 + -0.3333333334 = 0.2675918796 x2 = 0.2675918796 Simplifying x2 = 0.2675918796 Take the square root of each side: x = {-0.517292837, 0.517292837}Subproblem 2
x2 + 0.3333333334 = -0.600925213 Simplifying x2 + 0.3333333334 = -0.600925213 Reorder the terms: 0.3333333334 + x2 = -0.600925213 Solving 0.3333333334 + x2 = -0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x2 = -0.600925213 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x2 = -0.600925213 + -0.3333333334 x2 = -0.600925213 + -0.3333333334 Combine like terms: -0.600925213 + -0.3333333334 = -0.9342585464 x2 = -0.9342585464 Simplifying x2 = -0.9342585464 Reorder the terms: 0.9342585464 + x2 = -0.9342585464 + 0.9342585464 Combine like terms: -0.9342585464 + 0.9342585464 = 0.0000000000 0.9342585464 + x2 = 0.0000000000 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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