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Simplifying (4x + 1)(6x + -3) = 3x Reorder the terms: (1 + 4x)(6x + -3) = 3x Reorder the terms: (1 + 4x)(-3 + 6x) = 3x Multiply (1 + 4x) * (-3 + 6x) (1(-3 + 6x) + 4x * (-3 + 6x)) = 3x ((-3 * 1 + 6x * 1) + 4x * (-3 + 6x)) = 3x ((-3 + 6x) + 4x * (-3 + 6x)) = 3x (-3 + 6x + (-3 * 4x + 6x * 4x)) = 3x (-3 + 6x + (-12x + 24x2)) = 3x Combine like terms: 6x + -12x = -6x (-3 + -6x + 24x2) = 3x Solving -3 + -6x + 24x2 = 3x Solving for variable 'x'. Reorder the terms: -3 + -6x + -3x + 24x2 = 3x + -3x Combine like terms: -6x + -3x = -9x -3 + -9x + 24x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -3 + -9x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -3x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -3x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + -3x + 8x2 = 0 Solving -1 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.375x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.375x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.375x + x2 = 0 + 0.125 -0.375x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.375x + x2 = 0.125 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.125 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.125 + 0.03515625 Combine like terms: 0.125 + 0.03515625 = 0.16015625 0.03515625 + -0.375x + x2 = 0.16015625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.16015625 Calculate the square root of the right side: 0.400195265 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.400195265 and -0.400195265.Subproblem 1
x + -0.1875 = 0.400195265 Simplifying x + -0.1875 = 0.400195265 Reorder the terms: -0.1875 + x = 0.400195265 Solving -0.1875 + x = 0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.400195265 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.400195265 + 0.1875 x = 0.400195265 + 0.1875 Combine like terms: 0.400195265 + 0.1875 = 0.587695265 x = 0.587695265 Simplifying x = 0.587695265Subproblem 2
x + -0.1875 = -0.400195265 Simplifying x + -0.1875 = -0.400195265 Reorder the terms: -0.1875 + x = -0.400195265 Solving -0.1875 + x = -0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.400195265 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.400195265 + 0.1875 x = -0.400195265 + 0.1875 Combine like terms: -0.400195265 + 0.1875 = -0.212695265 x = -0.212695265 Simplifying x = -0.212695265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.587695265, -0.212695265}Solution
x = {0.587695265, -0.212695265}
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