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Simplifying 9(x) = 6x2 + -25x + -9 Reorder the terms: 9x = -9 + -25x + 6x2 Solving 9x = -9 + -25x + 6x2 Solving for variable 'x'. Reorder the terms: 9 + 9x + 25x + -6x2 = -9 + -25x + 6x2 + 9 + 25x + -6x2 Combine like terms: 9x + 25x = 34x 9 + 34x + -6x2 = -9 + -25x + 6x2 + 9 + 25x + -6x2 Reorder the terms: 9 + 34x + -6x2 = -9 + 9 + -25x + 25x + 6x2 + -6x2 Combine like terms: -9 + 9 = 0 9 + 34x + -6x2 = 0 + -25x + 25x + 6x2 + -6x2 9 + 34x + -6x2 = -25x + 25x + 6x2 + -6x2 Combine like terms: -25x + 25x = 0 9 + 34x + -6x2 = 0 + 6x2 + -6x2 9 + 34x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 9 + 34x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.5 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -5.666666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -5.666666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -5.666666667x + x2 = 0 + 1.5 -5.666666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -5.666666667x + x2 = 1.5 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 1.5 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 1.5 + 8.027777782 Combine like terms: 1.5 + 8.027777782 = 9.527777782 8.027777782 + -5.666666667x + x2 = 9.527777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 9.527777782 Calculate the square root of the right side: 3.086709864 Break this problem into two subproblems by setting (x + -2.833333334) equal to 3.086709864 and -3.086709864.Subproblem 1
x + -2.833333334 = 3.086709864 Simplifying x + -2.833333334 = 3.086709864 Reorder the terms: -2.833333334 + x = 3.086709864 Solving -2.833333334 + x = 3.086709864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 3.086709864 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.086709864 + 2.833333334 x = 3.086709864 + 2.833333334 Combine like terms: 3.086709864 + 2.833333334 = 5.920043198 x = 5.920043198 Simplifying x = 5.920043198Subproblem 2
x + -2.833333334 = -3.086709864 Simplifying x + -2.833333334 = -3.086709864 Reorder the terms: -2.833333334 + x = -3.086709864 Solving -2.833333334 + x = -3.086709864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -3.086709864 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.086709864 + 2.833333334 x = -3.086709864 + 2.833333334 Combine like terms: -3.086709864 + 2.833333334 = -0.25337653 x = -0.25337653 Simplifying x = -0.25337653Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.920043198, -0.25337653}
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