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Simplifying 9x2 + 24x + -34 = 0 Reorder the terms: -34 + 24x + 9x2 = 0 Solving -34 + 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'. -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 = 1.02368927 x = 1.02368927 Simplifying x = 1.02368927Subproblem 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 = -3.690355938 x = -3.690355938 Simplifying x = -3.690355938Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.02368927, -3.690355938}
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