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Simplifying 3x(2x + -5) = 8x + -9 Reorder the terms: 3x(-5 + 2x) = 8x + -9 (-5 * 3x + 2x * 3x) = 8x + -9 (-15x + 6x2) = 8x + -9 Reorder the terms: -15x + 6x2 = -9 + 8x Solving -15x + 6x2 = -9 + 8x Solving for variable 'x'. Reorder the terms: 9 + -15x + -8x + 6x2 = -9 + 8x + 9 + -8x Combine like terms: -15x + -8x = -23x 9 + -23x + 6x2 = -9 + 8x + 9 + -8x Reorder the terms: 9 + -23x + 6x2 = -9 + 9 + 8x + -8x Combine like terms: -9 + 9 = 0 9 + -23x + 6x2 = 0 + 8x + -8x 9 + -23x + 6x2 = 8x + -8x Combine like terms: 8x + -8x = 0 9 + -23x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.833333333x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.833333333x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.833333333x + x2 = 0 + -1.5 -3.833333333x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -3.833333333x + x2 = -1.5 The x term is -3.833333333x. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333x + 3.673611112 + x2 = -1.5 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = -1.5 + 3.673611112 Combine like terms: -1.5 + 3.673611112 = 2.173611112 3.673611112 + -3.833333333x + x2 = 2.173611112 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 2.173611112 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (x + -1.916666667) equal to 1.474317168 and -1.474317168.Subproblem 1
x + -1.916666667 = 1.474317168 Simplifying x + -1.916666667 = 1.474317168 Reorder the terms: -1.916666667 + x = 1.474317168 Solving -1.916666667 + x = 1.474317168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = 1.474317168 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 1.474317168 + 1.916666667 x = 1.474317168 + 1.916666667 Combine like terms: 1.474317168 + 1.916666667 = 3.390983835 x = 3.390983835 Simplifying x = 3.390983835Subproblem 2
x + -1.916666667 = -1.474317168 Simplifying x + -1.916666667 = -1.474317168 Reorder the terms: -1.916666667 + x = -1.474317168 Solving -1.916666667 + x = -1.474317168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = -1.474317168 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -1.474317168 + 1.916666667 x = -1.474317168 + 1.916666667 Combine like terms: -1.474317168 + 1.916666667 = 0.442349499 x = 0.442349499 Simplifying x = 0.442349499Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.390983835, 0.442349499}
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