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Simplifying (2x + -3)(3x + 2) = 18 Reorder the terms: (-3 + 2x)(3x + 2) = 18 Reorder the terms: (-3 + 2x)(2 + 3x) = 18 Multiply (-3 + 2x) * (2 + 3x) (-3(2 + 3x) + 2x * (2 + 3x)) = 18 ((2 * -3 + 3x * -3) + 2x * (2 + 3x)) = 18 ((-6 + -9x) + 2x * (2 + 3x)) = 18 (-6 + -9x + (2 * 2x + 3x * 2x)) = 18 (-6 + -9x + (4x + 6x2)) = 18 Combine like terms: -9x + 4x = -5x (-6 + -5x + 6x2) = 18 Solving -6 + -5x + 6x2 = 18 Solving for variable 'x'. Reorder the terms: -6 + -18 + -5x + 6x2 = 18 + -18 Combine like terms: -6 + -18 = -24 -24 + -5x + 6x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -24 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.8333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.8333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.8333333333x + x2 = 0 + 4 -0.8333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.8333333333x + x2 = 4 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 4 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 4 + 0.1736111111 Combine like terms: 4 + 0.1736111111 = 4.1736111111 0.1736111111 + -0.8333333333x + x2 = 4.1736111111 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 4.1736111111 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 2.042941779 and -2.042941779.Subproblem 1
x + -0.4166666667 = 2.042941779 Simplifying x + -0.4166666667 = 2.042941779 Reorder the terms: -0.4166666667 + x = 2.042941779 Solving -0.4166666667 + x = 2.042941779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 2.042941779 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 2.042941779 + 0.4166666667 x = 2.042941779 + 0.4166666667 Combine like terms: 2.042941779 + 0.4166666667 = 2.4596084457 x = 2.4596084457 Simplifying x = 2.4596084457Subproblem 2
x + -0.4166666667 = -2.042941779 Simplifying x + -0.4166666667 = -2.042941779 Reorder the terms: -0.4166666667 + x = -2.042941779 Solving -0.4166666667 + x = -2.042941779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -2.042941779 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -2.042941779 + 0.4166666667 x = -2.042941779 + 0.4166666667 Combine like terms: -2.042941779 + 0.4166666667 = -1.6262751123 x = -1.6262751123 Simplifying x = -1.6262751123Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4596084457, -1.6262751123}
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