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Simplifying 0 = 9x2 + 6x + 2 Reorder the terms: 0 = 2 + 6x + 9x2 Solving 0 = 2 + 6x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -6x + -9x2 = 2 + 6x + 9x2 + -2 + -6x + -9x2 Reorder the terms: -2 + -6x + -9x2 = 2 + -2 + 6x + -6x + 9x2 + -9x2 Combine like terms: 2 + -2 = 0 -2 + -6x + -9x2 = 0 + 6x + -6x + 9x2 + -9x2 -2 + -6x + -9x2 = 6x + -6x + 9x2 + -9x2 Combine like terms: 6x + -6x = 0 -2 + -6x + -9x2 = 0 + 9x2 + -9x2 -2 + -6x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -2 + -6x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 6x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 6x + 9x2)' equal to zero and attempt to solve: Simplifying 2 + 6x + 9x2 = 0 Solving 2 + 6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 0.6666666667x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 0.6666666667x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.2222222222 0.6666666667x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 0.6666666667x + x2 = -0.2222222222 The x term is 0.6666666667x. 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. 0.6666666667x + 0.1111111112 + x2 = -0.2222222222 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.2222222222 + 0.1111111112 Combine like terms: -0.2222222222 + 0.1111111112 = -0.111111111 0.1111111112 + 0.6666666667x + x2 = -0.111111111 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.111111111 Can't calculate square root of the right side. 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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