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Simplifying 0 = 9x2 + 6x + 45 Reorder the terms: 0 = 45 + 6x + 9x2 Solving 0 = 45 + 6x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + -6x + -9x2 = 45 + 6x + 9x2 + -45 + -6x + -9x2 Reorder the terms: -45 + -6x + -9x2 = 45 + -45 + 6x + -6x + 9x2 + -9x2 Combine like terms: 45 + -45 = 0 -45 + -6x + -9x2 = 0 + 6x + -6x + 9x2 + -9x2 -45 + -6x + -9x2 = 6x + -6x + 9x2 + -9x2 Combine like terms: 6x + -6x = 0 -45 + -6x + -9x2 = 0 + 9x2 + -9x2 -45 + -6x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -45 + -6x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(15 + 2x + 3x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(15 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying 15 + 2x + 3x2 = 0 Solving 15 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 0.6666666667x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 0.6666666667x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 0.6666666667x + x2 = 0 + -5 0.6666666667x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 0.6666666667x + x2 = -5 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 = -5 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -5 + 0.1111111112 Combine like terms: -5 + 0.1111111112 = -4.8888888888 0.1111111112 + 0.6666666667x + x2 = -4.8888888888 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -4.8888888888 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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