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Simplifying 9x2 + -31x + 24 = 0 Reorder the terms: 24 + -31x + 9x2 = 0 Solving 24 + -31x + 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'. 2.666666667 + -3.444444444x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -3.444444444x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -3.444444444x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -3.444444444x + x2 = 0 + -2.666666667 -3.444444444x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -3.444444444x + x2 = -2.666666667 The x term is -3.444444444x. Take half its coefficient (-1.722222222). Square it (2.966049382) and add it to both sides. Add '2.966049382' to each side of the equation. -3.444444444x + 2.966049382 + x2 = -2.666666667 + 2.966049382 Reorder the terms: 2.966049382 + -3.444444444x + x2 = -2.666666667 + 2.966049382 Combine like terms: -2.666666667 + 2.966049382 = 0.299382715 2.966049382 + -3.444444444x + x2 = 0.299382715 Factor a perfect square on the left side: (x + -1.722222222)(x + -1.722222222) = 0.299382715 Calculate the square root of the right side: 0.547158766 Break this problem into two subproblems by setting (x + -1.722222222) equal to 0.547158766 and -0.547158766.Subproblem 1
x + -1.722222222 = 0.547158766 Simplifying x + -1.722222222 = 0.547158766 Reorder the terms: -1.722222222 + x = 0.547158766 Solving -1.722222222 + x = 0.547158766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = 0.547158766 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = 0.547158766 + 1.722222222 x = 0.547158766 + 1.722222222 Combine like terms: 0.547158766 + 1.722222222 = 2.269380988 x = 2.269380988 Simplifying x = 2.269380988Subproblem 2
x + -1.722222222 = -0.547158766 Simplifying x + -1.722222222 = -0.547158766 Reorder the terms: -1.722222222 + x = -0.547158766 Solving -1.722222222 + x = -0.547158766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = -0.547158766 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = -0.547158766 + 1.722222222 x = -0.547158766 + 1.722222222 Combine like terms: -0.547158766 + 1.722222222 = 1.175063456 x = 1.175063456 Simplifying x = 1.175063456Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.269380988, 1.175063456}
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