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Simplifying 18x2 + 32x = -16 Reorder the terms: 32x + 18x2 = -16 Solving 32x + 18x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 32x + 18x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 32x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 16x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 16x + 9x2)' equal to zero and attempt to solve: Simplifying 8 + 16x + 9x2 = 0 Solving 8 + 16x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 1.777777778x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 1.777777778x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 1.777777778x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 1.777777778x + x2 = 0 + -0.8888888889 1.777777778x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 1.777777778x + x2 = -0.8888888889 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 = -0.8888888889 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778x + x2 = -0.8888888889 + 0.7901234570 Combine like terms: -0.8888888889 + 0.7901234570 = -0.0987654319 0.7901234570 + 1.777777778x + x2 = -0.0987654319 Factor a perfect square on the left side: (x + 0.888888889)(x + 0.888888889) = -0.0987654319 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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