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Simplifying 9x(-6x + 5) = 9x + -11 Reorder the terms: 9x(5 + -6x) = 9x + -11 (5 * 9x + -6x * 9x) = 9x + -11 (45x + -54x2) = 9x + -11 Reorder the terms: 45x + -54x2 = -11 + 9x Solving 45x + -54x2 = -11 + 9x Solving for variable 'x'. Reorder the terms: 11 + 45x + -9x + -54x2 = -11 + 9x + 11 + -9x Combine like terms: 45x + -9x = 36x 11 + 36x + -54x2 = -11 + 9x + 11 + -9x Reorder the terms: 11 + 36x + -54x2 = -11 + 11 + 9x + -9x Combine like terms: -11 + 11 = 0 11 + 36x + -54x2 = 0 + 9x + -9x 11 + 36x + -54x2 = 9x + -9x Combine like terms: 9x + -9x = 0 11 + 36x + -54x2 = 0 Begin completing the square. Divide all terms by -54 the coefficient of the squared term: Divide each side by '-54'. -0.2037037037 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.2037037037' to each side of the equation. -0.2037037037 + -0.6666666667x + 0.2037037037 + x2 = 0 + 0.2037037037 Reorder the terms: -0.2037037037 + 0.2037037037 + -0.6666666667x + x2 = 0 + 0.2037037037 Combine like terms: -0.2037037037 + 0.2037037037 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + 0.2037037037 -0.6666666667x + x2 = 0 + 0.2037037037 Combine like terms: 0 + 0.2037037037 = 0.2037037037 -0.6666666667x + x2 = 0.2037037037 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.2037037037 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.2037037037 + 0.1111111112 Combine like terms: 0.2037037037 + 0.1111111112 = 0.3148148149 0.1111111112 + -0.6666666667x + x2 = 0.3148148149 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.3148148149 Calculate the square root of the right side: 0.561083608 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.561083608 and -0.561083608.Subproblem 1
x + -0.3333333334 = 0.561083608 Simplifying x + -0.3333333334 = 0.561083608 Reorder the terms: -0.3333333334 + x = 0.561083608 Solving -0.3333333334 + x = 0.561083608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.561083608 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.561083608 + 0.3333333334 x = 0.561083608 + 0.3333333334 Combine like terms: 0.561083608 + 0.3333333334 = 0.8944169414 x = 0.8944169414 Simplifying x = 0.8944169414Subproblem 2
x + -0.3333333334 = -0.561083608 Simplifying x + -0.3333333334 = -0.561083608 Reorder the terms: -0.3333333334 + x = -0.561083608 Solving -0.3333333334 + x = -0.561083608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.561083608 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.561083608 + 0.3333333334 x = -0.561083608 + 0.3333333334 Combine like terms: -0.561083608 + 0.3333333334 = -0.2277502746 x = -0.2277502746 Simplifying x = -0.2277502746Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8944169414, -0.2277502746}
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