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Simplifying 0 = 9x2 + 16x + 80 Reorder the terms: 0 = 80 + 16x + 9x2 Solving 0 = 80 + 16x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + -16x + -9x2 = 80 + 16x + 9x2 + -80 + -16x + -9x2 Reorder the terms: -80 + -16x + -9x2 = 80 + -80 + 16x + -16x + 9x2 + -9x2 Combine like terms: 80 + -80 = 0 -80 + -16x + -9x2 = 0 + 16x + -16x + 9x2 + -9x2 -80 + -16x + -9x2 = 16x + -16x + 9x2 + -9x2 Combine like terms: 16x + -16x = 0 -80 + -16x + -9x2 = 0 + 9x2 + -9x2 -80 + -16x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -80 + -16x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(80 + 16x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(80 + 16x + 9x2)' equal to zero and attempt to solve: Simplifying 80 + 16x + 9x2 = 0 Solving 80 + 16x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 8.888888889 + 1.777777778x + x2 = 0 Move the constant term to the right: Add '-8.888888889' to each side of the equation. 8.888888889 + 1.777777778x + -8.888888889 + x2 = 0 + -8.888888889 Reorder the terms: 8.888888889 + -8.888888889 + 1.777777778x + x2 = 0 + -8.888888889 Combine like terms: 8.888888889 + -8.888888889 = 0.000000000 0.000000000 + 1.777777778x + x2 = 0 + -8.888888889 1.777777778x + x2 = 0 + -8.888888889 Combine like terms: 0 + -8.888888889 = -8.888888889 1.777777778x + x2 = -8.888888889 The x term is 1.777777778x. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778x + 0.7901234570 + x2 = -8.888888889 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778x + x2 = -8.888888889 + 0.7901234570 Combine like terms: -8.888888889 + 0.7901234570 = -8.098765432 0.7901234570 + 1.777777778x + x2 = -8.098765432 Factor a perfect square on the left side: (x + 0.888888889)(x + 0.888888889) = -8.098765432 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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