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Simplifying (17x2 + 15x + 9) + (19x2 + 13x + 5) = 0 Reorder the terms: (9 + 15x + 17x2) + (19x2 + 13x + 5) = 0 Remove parenthesis around (9 + 15x + 17x2) 9 + 15x + 17x2 + (19x2 + 13x + 5) = 0 Reorder the terms: 9 + 15x + 17x2 + (5 + 13x + 19x2) = 0 Remove parenthesis around (5 + 13x + 19x2) 9 + 15x + 17x2 + 5 + 13x + 19x2 = 0 Reorder the terms: 9 + 5 + 15x + 13x + 17x2 + 19x2 = 0 Combine like terms: 9 + 5 = 14 14 + 15x + 13x + 17x2 + 19x2 = 0 Combine like terms: 15x + 13x = 28x 14 + 28x + 17x2 + 19x2 = 0 Combine like terms: 17x2 + 19x2 = 36x2 14 + 28x + 36x2 = 0 Solving 14 + 28x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 14x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 14x + 18x2)' equal to zero and attempt to solve: Simplifying 7 + 14x + 18x2 = 0 Solving 7 + 14x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.3888888889 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '-0.3888888889' to each side of the equation. 0.3888888889 + 0.7777777778x + -0.3888888889 + x2 = 0 + -0.3888888889 Reorder the terms: 0.3888888889 + -0.3888888889 + 0.7777777778x + x2 = 0 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + -0.3888888889 0.7777777778x + x2 = 0 + -0.3888888889 Combine like terms: 0 + -0.3888888889 = -0.3888888889 0.7777777778x + x2 = -0.3888888889 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 = -0.3888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = -0.3888888889 + 0.1512345679 Combine like terms: -0.3888888889 + 0.1512345679 = -0.237654321 0.1512345679 + 0.7777777778x + x2 = -0.237654321 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = -0.237654321 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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