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Simplifying (6x + 1)(4x + -6) = 45 Reorder the terms: (1 + 6x)(4x + -6) = 45 Reorder the terms: (1 + 6x)(-6 + 4x) = 45 Multiply (1 + 6x) * (-6 + 4x) (1(-6 + 4x) + 6x * (-6 + 4x)) = 45 ((-6 * 1 + 4x * 1) + 6x * (-6 + 4x)) = 45 ((-6 + 4x) + 6x * (-6 + 4x)) = 45 (-6 + 4x + (-6 * 6x + 4x * 6x)) = 45 (-6 + 4x + (-36x + 24x2)) = 45 Combine like terms: 4x + -36x = -32x (-6 + -32x + 24x2) = 45 Solving -6 + -32x + 24x2 = 45 Solving for variable 'x'. Reorder the terms: -6 + -45 + -32x + 24x2 = 45 + -45 Combine like terms: -6 + -45 = -51 -51 + -32x + 24x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -51 + -32x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -2.125 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + -1.333333333x + 2.125 + x2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + -1.333333333x + x2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + -1.333333333x + x2 = 0 + 2.125 -1.333333333x + x2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 -1.333333333x + x2 = 2.125 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 2.125 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 2.125 + 0.4444444442 Combine like terms: 2.125 + 0.4444444442 = 2.5694444442 0.4444444442 + -1.333333333x + x2 = 2.5694444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 2.5694444442 Calculate the square root of the right side: 1.602948672 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.602948672 and -1.602948672.Subproblem 1
x + -0.6666666665 = 1.602948672 Simplifying x + -0.6666666665 = 1.602948672 Reorder the terms: -0.6666666665 + x = 1.602948672 Solving -0.6666666665 + x = 1.602948672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.602948672 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.602948672 + 0.6666666665 x = 1.602948672 + 0.6666666665 Combine like terms: 1.602948672 + 0.6666666665 = 2.2696153385 x = 2.2696153385 Simplifying x = 2.2696153385Subproblem 2
x + -0.6666666665 = -1.602948672 Simplifying x + -0.6666666665 = -1.602948672 Reorder the terms: -0.6666666665 + x = -1.602948672 Solving -0.6666666665 + x = -1.602948672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.602948672 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.602948672 + 0.6666666665 x = -1.602948672 + 0.6666666665 Combine like terms: -1.602948672 + 0.6666666665 = -0.9362820055 x = -0.9362820055 Simplifying x = -0.9362820055Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2696153385, -0.9362820055}
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