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Simplifying (3x + 1)(4x + -3) = 33 Reorder the terms: (1 + 3x)(4x + -3) = 33 Reorder the terms: (1 + 3x)(-3 + 4x) = 33 Multiply (1 + 3x) * (-3 + 4x) (1(-3 + 4x) + 3x * (-3 + 4x)) = 33 ((-3 * 1 + 4x * 1) + 3x * (-3 + 4x)) = 33 ((-3 + 4x) + 3x * (-3 + 4x)) = 33 (-3 + 4x + (-3 * 3x + 4x * 3x)) = 33 (-3 + 4x + (-9x + 12x2)) = 33 Combine like terms: 4x + -9x = -5x (-3 + -5x + 12x2) = 33 Solving -3 + -5x + 12x2 = 33 Solving for variable 'x'. Reorder the terms: -3 + -33 + -5x + 12x2 = 33 + -33 Combine like terms: -3 + -33 = -36 -36 + -5x + 12x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -36 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.4166666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.4166666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.4166666667x + x2 = 0 + 3 -0.4166666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.4166666667x + x2 = 3 The x term is -0.4166666667x. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667x + 0.04340277781 + x2 = 3 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 3 + 0.04340277781 Combine like terms: 3 + 0.04340277781 = 3.04340277781 0.04340277781 + -0.4166666667x + x2 = 3.04340277781 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 3.04340277781 Calculate the square root of the right side: 1.744535118 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 1.744535118 and -1.744535118.Subproblem 1
x + -0.2083333334 = 1.744535118 Simplifying x + -0.2083333334 = 1.744535118 Reorder the terms: -0.2083333334 + x = 1.744535118 Solving -0.2083333334 + x = 1.744535118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = 1.744535118 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 1.744535118 + 0.2083333334 x = 1.744535118 + 0.2083333334 Combine like terms: 1.744535118 + 0.2083333334 = 1.9528684514 x = 1.9528684514 Simplifying x = 1.9528684514Subproblem 2
x + -0.2083333334 = -1.744535118 Simplifying x + -0.2083333334 = -1.744535118 Reorder the terms: -0.2083333334 + x = -1.744535118 Solving -0.2083333334 + x = -1.744535118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + x = -1.744535118 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -1.744535118 + 0.2083333334 x = -1.744535118 + 0.2083333334 Combine like terms: -1.744535118 + 0.2083333334 = -1.5362017846 x = -1.5362017846 Simplifying x = -1.5362017846Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9528684514, -1.5362017846}
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