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Simplifying 0 = 6x2 + -16x + -9 Reorder the terms: 0 = -9 + -16x + 6x2 Solving 0 = -9 + -16x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + 16x + -6x2 = -9 + -16x + 6x2 + 9 + 16x + -6x2 Reorder the terms: 9 + 16x + -6x2 = -9 + 9 + -16x + 16x + 6x2 + -6x2 Combine like terms: -9 + 9 = 0 9 + 16x + -6x2 = 0 + -16x + 16x + 6x2 + -6x2 9 + 16x + -6x2 = -16x + 16x + 6x2 + -6x2 Combine like terms: -16x + 16x = 0 9 + 16x + -6x2 = 0 + 6x2 + -6x2 9 + 16x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 9 + 16x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.5 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.666666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.666666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.666666667x + x2 = 0 + 1.5 -2.666666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.666666667x + x2 = 1.5 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 = 1.5 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 1.5 + 1.777777780 Combine like terms: 1.5 + 1.777777780 = 3.27777778 1.777777780 + -2.666666667x + x2 = 3.27777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 3.27777778 Calculate the square root of the right side: 1.810463416 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.810463416 and -1.810463416.Subproblem 1
x + -1.333333334 = 1.810463416 Simplifying x + -1.333333334 = 1.810463416 Reorder the terms: -1.333333334 + x = 1.810463416 Solving -1.333333334 + x = 1.810463416 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 = 1.810463416 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.810463416 + 1.333333334 x = 1.810463416 + 1.333333334 Combine like terms: 1.810463416 + 1.333333334 = 3.14379675 x = 3.14379675 Simplifying x = 3.14379675Subproblem 2
x + -1.333333334 = -1.810463416 Simplifying x + -1.333333334 = -1.810463416 Reorder the terms: -1.333333334 + x = -1.810463416 Solving -1.333333334 + x = -1.810463416 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 = -1.810463416 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.810463416 + 1.333333334 x = -1.810463416 + 1.333333334 Combine like terms: -1.810463416 + 1.333333334 = -0.477130082 x = -0.477130082 Simplifying x = -0.477130082Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.14379675, -0.477130082}
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