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Simplifying 9x4 = 6x2 + 1 Reorder the terms: 9x4 = 1 + 6x2 Solving 9x4 = 1 + 6x2 Solving for variable 'x'. Reorder the terms: -1 + -6x2 + 9x4 = 1 + 6x2 + -1 + -6x2 Reorder the terms: -1 + -6x2 + 9x4 = 1 + -1 + 6x2 + -6x2 Combine like terms: 1 + -1 = 0 -1 + -6x2 + 9x4 = 0 + 6x2 + -6x2 -1 + -6x2 + 9x4 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -1 + -6x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + -0.6666666667x2 + x4 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.6666666667x2 + 0.1111111111 + x4 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.6666666667x2 + x4 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.6666666667x2 + x4 = 0 + 0.1111111111 -0.6666666667x2 + x4 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.6666666667x2 + x4 = 0.1111111111 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 = 0.1111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x2 + x4 = 0.1111111111 + 0.1111111112 Combine like terms: 0.1111111111 + 0.1111111112 = 0.2222222223 0.1111111112 + -0.6666666667x2 + x4 = 0.2222222223 Factor a perfect square on the left side: (x2 + -0.3333333334)(x2 + -0.3333333334) = 0.2222222223 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (x2 + -0.3333333334) equal to 0.471404521 and -0.471404521.Subproblem 1
x2 + -0.3333333334 = 0.471404521 Simplifying x2 + -0.3333333334 = 0.471404521 Reorder the terms: -0.3333333334 + x2 = 0.471404521 Solving -0.3333333334 + x2 = 0.471404521 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 = 0.471404521 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x2 = 0.471404521 + 0.3333333334 x2 = 0.471404521 + 0.3333333334 Combine like terms: 0.471404521 + 0.3333333334 = 0.8047378544 x2 = 0.8047378544 Simplifying x2 = 0.8047378544 Take the square root of each side: x = {-0.897071822, 0.897071822}Subproblem 2
x2 + -0.3333333334 = -0.471404521 Simplifying x2 + -0.3333333334 = -0.471404521 Reorder the terms: -0.3333333334 + x2 = -0.471404521 Solving -0.3333333334 + x2 = -0.471404521 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 = -0.471404521 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x2 = -0.471404521 + 0.3333333334 x2 = -0.471404521 + 0.3333333334 Combine like terms: -0.471404521 + 0.3333333334 = -0.1380711876 x2 = -0.1380711876 Simplifying x2 = -0.1380711876 Reorder the terms: 0.1380711876 + x2 = -0.1380711876 + 0.1380711876 Combine like terms: -0.1380711876 + 0.1380711876 = 0.0000000000 0.1380711876 + 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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