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Simplifying 9X2 + -24X = 14 Reorder the terms: -24X + 9X2 = 14 Solving -24X + 9X2 = 14 Solving for variable 'X'. Reorder the terms: -14 + -24X + 9X2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -24X + 9X2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + -2.666666667X + X2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + -2.666666667X + 1.555555556 + X2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + -2.666666667X + X2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + -2.666666667X + X2 = 0 + 1.555555556 -2.666666667X + X2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 -2.666666667X + X2 = 1.555555556 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 = 1.555555556 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667X + X2 = 1.555555556 + 1.777777780 Combine like terms: 1.555555556 + 1.777777780 = 3.333333336 1.777777780 + -2.666666667X + X2 = 3.333333336 Factor a perfect square on the left side: (X + -1.333333334)(X + -1.333333334) = 3.333333336 Calculate the square root of the right side: 1.825741859 Break this problem into two subproblems by setting (X + -1.333333334) equal to 1.825741859 and -1.825741859.Subproblem 1
X + -1.333333334 = 1.825741859 Simplifying X + -1.333333334 = 1.825741859 Reorder the terms: -1.333333334 + X = 1.825741859 Solving -1.333333334 + X = 1.825741859 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 = 1.825741859 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + X = 1.825741859 + 1.333333334 X = 1.825741859 + 1.333333334 Combine like terms: 1.825741859 + 1.333333334 = 3.159075193 X = 3.159075193 Simplifying X = 3.159075193Subproblem 2
X + -1.333333334 = -1.825741859 Simplifying X + -1.333333334 = -1.825741859 Reorder the terms: -1.333333334 + X = -1.825741859 Solving -1.333333334 + X = -1.825741859 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 = -1.825741859 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + X = -1.825741859 + 1.333333334 X = -1.825741859 + 1.333333334 Combine like terms: -1.825741859 + 1.333333334 = -0.492408525 X = -0.492408525 Simplifying X = -0.492408525Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.159075193, -0.492408525}
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