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Simplifying 9x2 + -24x + 16 = 50 Reorder the terms: 16 + -24x + 9x2 = 50 Solving 16 + -24x + 9x2 = 50 Solving for variable 'x'. Reorder the terms: 16 + -50 + -24x + 9x2 = 50 + -50 Combine like terms: 16 + -50 = -34 -34 + -24x + 9x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -34 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.777777778 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '3.777777778' to each side of the equation. -3.777777778 + -2.666666667x + 3.777777778 + x2 = 0 + 3.777777778 Reorder the terms: -3.777777778 + 3.777777778 + -2.666666667x + x2 = 0 + 3.777777778 Combine like terms: -3.777777778 + 3.777777778 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 3.777777778 -2.666666667x + x2 = 0 + 3.777777778 Combine like terms: 0 + 3.777777778 = 3.777777778 -2.666666667x + x2 = 3.777777778 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 = 3.777777778 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 3.777777778 + 1.777777780 Combine like terms: 3.777777778 + 1.777777780 = 5.555555558 1.777777780 + -2.666666667x + x2 = 5.555555558 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 5.555555558 Calculate the square root of the right side: 2.357022604 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.357022604 and -2.357022604.Subproblem 1
x + -1.333333334 = 2.357022604 Simplifying x + -1.333333334 = 2.357022604 Reorder the terms: -1.333333334 + x = 2.357022604 Solving -1.333333334 + x = 2.357022604 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 = 2.357022604 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.357022604 + 1.333333334 x = 2.357022604 + 1.333333334 Combine like terms: 2.357022604 + 1.333333334 = 3.690355938 x = 3.690355938 Simplifying x = 3.690355938Subproblem 2
x + -1.333333334 = -2.357022604 Simplifying x + -1.333333334 = -2.357022604 Reorder the terms: -1.333333334 + x = -2.357022604 Solving -1.333333334 + x = -2.357022604 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 = -2.357022604 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.357022604 + 1.333333334 x = -2.357022604 + 1.333333334 Combine like terms: -2.357022604 + 1.333333334 = -1.02368927 x = -1.02368927 Simplifying x = -1.02368927Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.690355938, -1.02368927}
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