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Simplifying (9x + -2)(5x + 6) = x Reorder the terms: (-2 + 9x)(5x + 6) = x Reorder the terms: (-2 + 9x)(6 + 5x) = x Multiply (-2 + 9x) * (6 + 5x) (-2(6 + 5x) + 9x * (6 + 5x)) = x ((6 * -2 + 5x * -2) + 9x * (6 + 5x)) = x ((-12 + -10x) + 9x * (6 + 5x)) = x (-12 + -10x + (6 * 9x + 5x * 9x)) = x (-12 + -10x + (54x + 45x2)) = x Combine like terms: -10x + 54x = 44x (-12 + 44x + 45x2) = x Solving -12 + 44x + 45x2 = x Solving for variable 'x'. Reorder the terms: -12 + 44x + -1x + 45x2 = x + -1x Combine like terms: 44x + -1x = 43x -12 + 43x + 45x2 = x + -1x Combine like terms: x + -1x = 0 -12 + 43x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.2666666667 + 0.9555555556x + x2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.9555555556x + 0.2666666667 + x2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + 0.9555555556x + x2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + 0.9555555556x + x2 = 0 + 0.2666666667 0.9555555556x + x2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 0.9555555556x + x2 = 0.2666666667 The x term is 0.9555555556x. Take half its coefficient (0.4777777778). Square it (0.2282716050) and add it to both sides. Add '0.2282716050' to each side of the equation. 0.9555555556x + 0.2282716050 + x2 = 0.2666666667 + 0.2282716050 Reorder the terms: 0.2282716050 + 0.9555555556x + x2 = 0.2666666667 + 0.2282716050 Combine like terms: 0.2666666667 + 0.2282716050 = 0.4949382717 0.2282716050 + 0.9555555556x + x2 = 0.4949382717 Factor a perfect square on the left side: (x + 0.4777777778)(x + 0.4777777778) = 0.4949382717 Calculate the square root of the right side: 0.703518494 Break this problem into two subproblems by setting (x + 0.4777777778) equal to 0.703518494 and -0.703518494.Subproblem 1
x + 0.4777777778 = 0.703518494 Simplifying x + 0.4777777778 = 0.703518494 Reorder the terms: 0.4777777778 + x = 0.703518494 Solving 0.4777777778 + x = 0.703518494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4777777778' to each side of the equation. 0.4777777778 + -0.4777777778 + x = 0.703518494 + -0.4777777778 Combine like terms: 0.4777777778 + -0.4777777778 = 0.0000000000 0.0000000000 + x = 0.703518494 + -0.4777777778 x = 0.703518494 + -0.4777777778 Combine like terms: 0.703518494 + -0.4777777778 = 0.2257407162 x = 0.2257407162 Simplifying x = 0.2257407162Subproblem 2
x + 0.4777777778 = -0.703518494 Simplifying x + 0.4777777778 = -0.703518494 Reorder the terms: 0.4777777778 + x = -0.703518494 Solving 0.4777777778 + x = -0.703518494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4777777778' to each side of the equation. 0.4777777778 + -0.4777777778 + x = -0.703518494 + -0.4777777778 Combine like terms: 0.4777777778 + -0.4777777778 = 0.0000000000 0.0000000000 + x = -0.703518494 + -0.4777777778 x = -0.703518494 + -0.4777777778 Combine like terms: -0.703518494 + -0.4777777778 = -1.1812962718 x = -1.1812962718 Simplifying x = -1.1812962718Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2257407162, -1.1812962718}
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