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Simplifying -9x2 + 24x + 44 = 0 Reorder the terms: 44 + 24x + -9x2 = 0 Solving 44 + 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'. -4.888888889 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '4.888888889' to each side of the equation. -4.888888889 + -2.666666667x + 4.888888889 + x2 = 0 + 4.888888889 Reorder the terms: -4.888888889 + 4.888888889 + -2.666666667x + x2 = 0 + 4.888888889 Combine like terms: -4.888888889 + 4.888888889 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 4.888888889 -2.666666667x + x2 = 0 + 4.888888889 Combine like terms: 0 + 4.888888889 = 4.888888889 -2.666666667x + x2 = 4.888888889 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 = 4.888888889 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 4.888888889 + 1.777777780 Combine like terms: 4.888888889 + 1.777777780 = 6.666666669 1.777777780 + -2.666666667x + x2 = 6.666666669 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 6.666666669 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.581988898 and -2.581988898.Subproblem 1
x + -1.333333334 = 2.581988898 Simplifying x + -1.333333334 = 2.581988898 Reorder the terms: -1.333333334 + x = 2.581988898 Solving -1.333333334 + x = 2.581988898 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 = 2.581988898 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.581988898 + 1.333333334 x = 2.581988898 + 1.333333334 Combine like terms: 2.581988898 + 1.333333334 = 3.915322232 x = 3.915322232 Simplifying x = 3.915322232Subproblem 2
x + -1.333333334 = -2.581988898 Simplifying x + -1.333333334 = -2.581988898 Reorder the terms: -1.333333334 + x = -2.581988898 Solving -1.333333334 + x = -2.581988898 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 = -2.581988898 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.581988898 + 1.333333334 x = -2.581988898 + 1.333333334 Combine like terms: -2.581988898 + 1.333333334 = -1.248655564 x = -1.248655564 Simplifying x = -1.248655564Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.915322232, -1.248655564}
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