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Simplifying 0 = 9x2 + 7x + 8 Reorder the terms: 0 = 8 + 7x + 9x2 Solving 0 = 8 + 7x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -7x + -9x2 = 8 + 7x + 9x2 + -8 + -7x + -9x2 Reorder the terms: -8 + -7x + -9x2 = 8 + -8 + 7x + -7x + 9x2 + -9x2 Combine like terms: 8 + -8 = 0 -8 + -7x + -9x2 = 0 + 7x + -7x + 9x2 + -9x2 -8 + -7x + -9x2 = 7x + -7x + 9x2 + -9x2 Combine like terms: 7x + -7x = 0 -8 + -7x + -9x2 = 0 + 9x2 + -9x2 -8 + -7x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -8 + -7x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 7x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 7x + 9x2)' equal to zero and attempt to solve: Simplifying 8 + 7x + 9x2 = 0 Solving 8 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 0.7777777778x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 0.7777777778x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + -0.8888888889 0.7777777778x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 0.7777777778x + x2 = -0.8888888889 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = -0.8888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = -0.8888888889 + 0.1512345679 Combine like terms: -0.8888888889 + 0.1512345679 = -0.737654321 0.1512345679 + 0.7777777778x + x2 = -0.737654321 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = -0.737654321 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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