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Simplifying 0 = 14x2 + 5x + 9 Reorder the terms: 0 = 9 + 5x + 14x2 Solving 0 = 9 + 5x + 14x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -5x + -14x2 = 9 + 5x + 14x2 + -9 + -5x + -14x2 Reorder the terms: -9 + -5x + -14x2 = 9 + -9 + 5x + -5x + 14x2 + -14x2 Combine like terms: 9 + -9 = 0 -9 + -5x + -14x2 = 0 + 5x + -5x + 14x2 + -14x2 -9 + -5x + -14x2 = 5x + -5x + 14x2 + -14x2 Combine like terms: 5x + -5x = 0 -9 + -5x + -14x2 = 0 + 14x2 + -14x2 -9 + -5x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -9 + -5x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 5x + 14x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 5x + 14x2)' equal to zero and attempt to solve: Simplifying 9 + 5x + 14x2 = 0 Solving 9 + 5x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.6428571429 + 0.3571428571x + x2 = 0 Move the constant term to the right: Add '-0.6428571429' to each side of the equation. 0.6428571429 + 0.3571428571x + -0.6428571429 + x2 = 0 + -0.6428571429 Reorder the terms: 0.6428571429 + -0.6428571429 + 0.3571428571x + x2 = 0 + -0.6428571429 Combine like terms: 0.6428571429 + -0.6428571429 = 0.0000000000 0.0000000000 + 0.3571428571x + x2 = 0 + -0.6428571429 0.3571428571x + x2 = 0 + -0.6428571429 Combine like terms: 0 + -0.6428571429 = -0.6428571429 0.3571428571x + x2 = -0.6428571429 The x term is 0.3571428571x. Take half its coefficient (0.1785714286). Square it (0.03188775511) and add it to both sides. Add '0.03188775511' to each side of the equation. 0.3571428571x + 0.03188775511 + x2 = -0.6428571429 + 0.03188775511 Reorder the terms: 0.03188775511 + 0.3571428571x + x2 = -0.6428571429 + 0.03188775511 Combine like terms: -0.6428571429 + 0.03188775511 = -0.61096938779 0.03188775511 + 0.3571428571x + x2 = -0.61096938779 Factor a perfect square on the left side: (x + 0.1785714286)(x + 0.1785714286) = -0.61096938779 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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