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Simplifying 3x(x + -1) + 2(x + 6) = 54 Reorder the terms: 3x(-1 + x) + 2(x + 6) = 54 (-1 * 3x + x * 3x) + 2(x + 6) = 54 (-3x + 3x2) + 2(x + 6) = 54 Reorder the terms: -3x + 3x2 + 2(6 + x) = 54 -3x + 3x2 + (6 * 2 + x * 2) = 54 -3x + 3x2 + (12 + 2x) = 54 Reorder the terms: 12 + -3x + 2x + 3x2 = 54 Combine like terms: -3x + 2x = -1x 12 + -1x + 3x2 = 54 Solving 12 + -1x + 3x2 = 54 Solving for variable 'x'. Reorder the terms: 12 + -54 + -1x + 3x2 = 54 + -54 Combine like terms: 12 + -54 = -42 -42 + -1x + 3x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -42 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -0.3333333333x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -0.3333333333x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -0.3333333333x + x2 = 0 + 14 -0.3333333333x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -0.3333333333x + x2 = 14 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 14 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 14 + 0.02777777779 Combine like terms: 14 + 0.02777777779 = 14.02777777779 0.02777777779 + -0.3333333333x + x2 = 14.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 14.02777777779 Calculate the square root of the right side: 3.745367509 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 3.745367509 and -3.745367509.Subproblem 1
x + -0.1666666667 = 3.745367509 Simplifying x + -0.1666666667 = 3.745367509 Reorder the terms: -0.1666666667 + x = 3.745367509 Solving -0.1666666667 + x = 3.745367509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 3.745367509 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 3.745367509 + 0.1666666667 x = 3.745367509 + 0.1666666667 Combine like terms: 3.745367509 + 0.1666666667 = 3.9120341757 x = 3.9120341757 Simplifying x = 3.9120341757Subproblem 2
x + -0.1666666667 = -3.745367509 Simplifying x + -0.1666666667 = -3.745367509 Reorder the terms: -0.1666666667 + x = -3.745367509 Solving -0.1666666667 + x = -3.745367509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -3.745367509 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -3.745367509 + 0.1666666667 x = -3.745367509 + 0.1666666667 Combine like terms: -3.745367509 + 0.1666666667 = -3.5787008423 x = -3.5787008423 Simplifying x = -3.5787008423Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9120341757, -3.5787008423}
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