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Simplifying 9x2 + -34x + -204 = 0 Reorder the terms: -204 + -34x + 9x2 = 0 Solving -204 + -34x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -22.66666667 + -3.777777778x + x2 = 0 Move the constant term to the right: Add '22.66666667' to each side of the equation. -22.66666667 + -3.777777778x + 22.66666667 + x2 = 0 + 22.66666667 Reorder the terms: -22.66666667 + 22.66666667 + -3.777777778x + x2 = 0 + 22.66666667 Combine like terms: -22.66666667 + 22.66666667 = 0.00000000 0.00000000 + -3.777777778x + x2 = 0 + 22.66666667 -3.777777778x + x2 = 0 + 22.66666667 Combine like terms: 0 + 22.66666667 = 22.66666667 -3.777777778x + x2 = 22.66666667 The x term is -3.777777778x. Take half its coefficient (-1.888888889). Square it (3.567901235) and add it to both sides. Add '3.567901235' to each side of the equation. -3.777777778x + 3.567901235 + x2 = 22.66666667 + 3.567901235 Reorder the terms: 3.567901235 + -3.777777778x + x2 = 22.66666667 + 3.567901235 Combine like terms: 22.66666667 + 3.567901235 = 26.234567905 3.567901235 + -3.777777778x + x2 = 26.234567905 Factor a perfect square on the left side: (x + -1.888888889)(x + -1.888888889) = 26.234567905 Calculate the square root of the right side: 5.121969143 Break this problem into two subproblems by setting (x + -1.888888889) equal to 5.121969143 and -5.121969143.Subproblem 1
x + -1.888888889 = 5.121969143 Simplifying x + -1.888888889 = 5.121969143 Reorder the terms: -1.888888889 + x = 5.121969143 Solving -1.888888889 + x = 5.121969143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = 5.121969143 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = 5.121969143 + 1.888888889 x = 5.121969143 + 1.888888889 Combine like terms: 5.121969143 + 1.888888889 = 7.010858032 x = 7.010858032 Simplifying x = 7.010858032Subproblem 2
x + -1.888888889 = -5.121969143 Simplifying x + -1.888888889 = -5.121969143 Reorder the terms: -1.888888889 + x = -5.121969143 Solving -1.888888889 + x = -5.121969143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = -5.121969143 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = -5.121969143 + 1.888888889 x = -5.121969143 + 1.888888889 Combine like terms: -5.121969143 + 1.888888889 = -3.233080254 x = -3.233080254 Simplifying x = -3.233080254Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.010858032, -3.233080254}
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