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Simplifying 9x2 + -24x = 16 Reorder the terms: -24x + 9x2 = 16 Solving -24x + 9x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -24x + 9x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -2.666666667x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -2.666666667x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 1.777777778 -2.666666667x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -2.666666667x + x2 = 1.777777778 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 = 1.777777778 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 1.777777778 + 1.777777780 Combine like terms: 1.777777778 + 1.777777780 = 3.555555558 1.777777780 + -2.666666667x + x2 = 3.555555558 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 3.555555558 Calculate the square root of the right side: 1.885618084 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.885618084 and -1.885618084.Subproblem 1
x + -1.333333334 = 1.885618084 Simplifying x + -1.333333334 = 1.885618084 Reorder the terms: -1.333333334 + x = 1.885618084 Solving -1.333333334 + x = 1.885618084 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 = 1.885618084 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.885618084 + 1.333333334 x = 1.885618084 + 1.333333334 Combine like terms: 1.885618084 + 1.333333334 = 3.218951418 x = 3.218951418 Simplifying x = 3.218951418Subproblem 2
x + -1.333333334 = -1.885618084 Simplifying x + -1.333333334 = -1.885618084 Reorder the terms: -1.333333334 + x = -1.885618084 Solving -1.333333334 + x = -1.885618084 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 = -1.885618084 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.885618084 + 1.333333334 x = -1.885618084 + 1.333333334 Combine like terms: -1.885618084 + 1.333333334 = -0.55228475 x = -0.55228475 Simplifying x = -0.55228475Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.218951418, -0.55228475}
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