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Simplifying 9x2 + -24x + -28 = 0 Reorder the terms: -28 + -24x + 9x2 = 0 Solving -28 + -24x + 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'. -3.111111111 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + -2.666666667x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + -2.666666667x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 3.111111111 -2.666666667x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 -2.666666667x + x2 = 3.111111111 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 3.111111111 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 3.111111111 + 1.777777780 Combine like terms: 3.111111111 + 1.777777780 = 4.888888891 1.777777780 + -2.666666667x + x2 = 4.888888891 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 4.888888891 Calculate the square root of the right side: 2.211083194 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.211083194 and -2.211083194.Subproblem 1
x + -1.333333334 = 2.211083194 Simplifying x + -1.333333334 = 2.211083194 Reorder the terms: -1.333333334 + x = 2.211083194 Solving -1.333333334 + x = 2.211083194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 2.211083194 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.211083194 + 1.333333334 x = 2.211083194 + 1.333333334 Combine like terms: 2.211083194 + 1.333333334 = 3.544416528 x = 3.544416528 Simplifying x = 3.544416528Subproblem 2
x + -1.333333334 = -2.211083194 Simplifying x + -1.333333334 = -2.211083194 Reorder the terms: -1.333333334 + x = -2.211083194 Solving -1.333333334 + x = -2.211083194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -2.211083194 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.211083194 + 1.333333334 x = -2.211083194 + 1.333333334 Combine like terms: -2.211083194 + 1.333333334 = -0.87774986 x = -0.87774986 Simplifying x = -0.87774986Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.544416528, -0.87774986}
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