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Simplifying 9x2 + -33x + 25 = 0 Reorder the terms: 25 + -33x + 9x2 = 0 Solving 25 + -33x + 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'. 2.777777778 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + -3.666666667x + -2.777777778 + x2 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + -3.666666667x + x2 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + -2.777777778 -3.666666667x + x2 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 -3.666666667x + x2 = -2.777777778 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = -2.777777778 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -2.777777778 + 3.361111114 Combine like terms: -2.777777778 + 3.361111114 = 0.583333336 3.361111114 + -3.666666667x + x2 = 0.583333336 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 0.583333336 Calculate the square root of the right side: 0.763762618 Break this problem into two subproblems by setting (x + -1.833333334) equal to 0.763762618 and -0.763762618.Subproblem 1
x + -1.833333334 = 0.763762618 Simplifying x + -1.833333334 = 0.763762618 Reorder the terms: -1.833333334 + x = 0.763762618 Solving -1.833333334 + x = 0.763762618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 0.763762618 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 0.763762618 + 1.833333334 x = 0.763762618 + 1.833333334 Combine like terms: 0.763762618 + 1.833333334 = 2.597095952 x = 2.597095952 Simplifying x = 2.597095952Subproblem 2
x + -1.833333334 = -0.763762618 Simplifying x + -1.833333334 = -0.763762618 Reorder the terms: -1.833333334 + x = -0.763762618 Solving -1.833333334 + x = -0.763762618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -0.763762618 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -0.763762618 + 1.833333334 x = -0.763762618 + 1.833333334 Combine like terms: -0.763762618 + 1.833333334 = 1.069570716 x = 1.069570716 Simplifying x = 1.069570716Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.597095952, 1.069570716}
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