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Simplifying 9x(3x + -5) = 4x + -1(7 + -6x) Reorder the terms: 9x(-5 + 3x) = 4x + -1(7 + -6x) (-5 * 9x + 3x * 9x) = 4x + -1(7 + -6x) (-45x + 27x2) = 4x + -1(7 + -6x) -45x + 27x2 = 4x + (7 * -1 + -6x * -1) -45x + 27x2 = 4x + (-7 + 6x) Reorder the terms: -45x + 27x2 = -7 + 4x + 6x Combine like terms: 4x + 6x = 10x -45x + 27x2 = -7 + 10x Solving -45x + 27x2 = -7 + 10x Solving for variable 'x'. Reorder the terms: 7 + -45x + -10x + 27x2 = -7 + 10x + 7 + -10x Combine like terms: -45x + -10x = -55x 7 + -55x + 27x2 = -7 + 10x + 7 + -10x Reorder the terms: 7 + -55x + 27x2 = -7 + 7 + 10x + -10x Combine like terms: -7 + 7 = 0 7 + -55x + 27x2 = 0 + 10x + -10x 7 + -55x + 27x2 = 10x + -10x Combine like terms: 10x + -10x = 0 7 + -55x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.2592592593 + -2.037037037x + x2 = 0 Move the constant term to the right: Add '-0.2592592593' to each side of the equation. 0.2592592593 + -2.037037037x + -0.2592592593 + x2 = 0 + -0.2592592593 Reorder the terms: 0.2592592593 + -0.2592592593 + -2.037037037x + x2 = 0 + -0.2592592593 Combine like terms: 0.2592592593 + -0.2592592593 = 0.0000000000 0.0000000000 + -2.037037037x + x2 = 0 + -0.2592592593 -2.037037037x + x2 = 0 + -0.2592592593 Combine like terms: 0 + -0.2592592593 = -0.2592592593 -2.037037037x + x2 = -0.2592592593 The x term is -2.037037037x. Take half its coefficient (-1.018518519). Square it (1.037379974) and add it to both sides. Add '1.037379974' to each side of the equation. -2.037037037x + 1.037379974 + x2 = -0.2592592593 + 1.037379974 Reorder the terms: 1.037379974 + -2.037037037x + x2 = -0.2592592593 + 1.037379974 Combine like terms: -0.2592592593 + 1.037379974 = 0.7781207147 1.037379974 + -2.037037037x + x2 = 0.7781207147 Factor a perfect square on the left side: (x + -1.018518519)(x + -1.018518519) = 0.7781207147 Calculate the square root of the right side: 0.882111509 Break this problem into two subproblems by setting (x + -1.018518519) equal to 0.882111509 and -0.882111509.Subproblem 1
x + -1.018518519 = 0.882111509 Simplifying x + -1.018518519 = 0.882111509 Reorder the terms: -1.018518519 + x = 0.882111509 Solving -1.018518519 + x = 0.882111509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.018518519' to each side of the equation. -1.018518519 + 1.018518519 + x = 0.882111509 + 1.018518519 Combine like terms: -1.018518519 + 1.018518519 = 0.000000000 0.000000000 + x = 0.882111509 + 1.018518519 x = 0.882111509 + 1.018518519 Combine like terms: 0.882111509 + 1.018518519 = 1.900630028 x = 1.900630028 Simplifying x = 1.900630028Subproblem 2
x + -1.018518519 = -0.882111509 Simplifying x + -1.018518519 = -0.882111509 Reorder the terms: -1.018518519 + x = -0.882111509 Solving -1.018518519 + x = -0.882111509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.018518519' to each side of the equation. -1.018518519 + 1.018518519 + x = -0.882111509 + 1.018518519 Combine like terms: -1.018518519 + 1.018518519 = 0.000000000 0.000000000 + x = -0.882111509 + 1.018518519 x = -0.882111509 + 1.018518519 Combine like terms: -0.882111509 + 1.018518519 = 0.13640701 x = 0.13640701 Simplifying x = 0.13640701Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.900630028, 0.13640701}
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