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Simplifying (3x2 + 2x + -9) + -1(-3x + 4) = 0 Reorder the terms: (-9 + 2x + 3x2) + -1(-3x + 4) = 0 Remove parenthesis around (-9 + 2x + 3x2) -9 + 2x + 3x2 + -1(-3x + 4) = 0 Reorder the terms: -9 + 2x + 3x2 + -1(4 + -3x) = 0 -9 + 2x + 3x2 + (4 * -1 + -3x * -1) = 0 -9 + 2x + 3x2 + (-4 + 3x) = 0 Reorder the terms: -9 + -4 + 2x + 3x + 3x2 = 0 Combine like terms: -9 + -4 = -13 -13 + 2x + 3x + 3x2 = 0 Combine like terms: 2x + 3x = 5x -13 + 5x + 3x2 = 0 Solving -13 + 5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + 1.666666667x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + 1.666666667x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 4.333333333 1.666666667x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 1.666666667x + x2 = 4.333333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 4.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 4.333333333 + 0.6944444447 Combine like terms: 4.333333333 + 0.6944444447 = 5.0277777777 0.6944444447 + 1.666666667x + x2 = 5.0277777777 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 5.0277777777 Calculate the square root of the right side: 2.242270674 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.242270674 and -2.242270674.Subproblem 1
x + 0.8333333335 = 2.242270674 Simplifying x + 0.8333333335 = 2.242270674 Reorder the terms: 0.8333333335 + x = 2.242270674 Solving 0.8333333335 + x = 2.242270674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 2.242270674 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.242270674 + -0.8333333335 x = 2.242270674 + -0.8333333335 Combine like terms: 2.242270674 + -0.8333333335 = 1.4089373405 x = 1.4089373405 Simplifying x = 1.4089373405Subproblem 2
x + 0.8333333335 = -2.242270674 Simplifying x + 0.8333333335 = -2.242270674 Reorder the terms: 0.8333333335 + x = -2.242270674 Solving 0.8333333335 + x = -2.242270674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -2.242270674 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.242270674 + -0.8333333335 x = -2.242270674 + -0.8333333335 Combine like terms: -2.242270674 + -0.8333333335 = -3.0756040075 x = -3.0756040075 Simplifying x = -3.0756040075Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4089373405, -3.0756040075}
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