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Simplifying (3x + 1)(4x + -3) = 136 Reorder the terms: (1 + 3x)(4x + -3) = 136 Reorder the terms: (1 + 3x)(-3 + 4x) = 136 Multiply (1 + 3x) * (-3 + 4x) (1(-3 + 4x) + 3x * (-3 + 4x)) = 136 ((-3 * 1 + 4x * 1) + 3x * (-3 + 4x)) = 136 ((-3 + 4x) + 3x * (-3 + 4x)) = 136 (-3 + 4x + (-3 * 3x + 4x * 3x)) = 136 (-3 + 4x + (-9x + 12x2)) = 136 Combine like terms: 4x + -9x = -5x (-3 + -5x + 12x2) = 136 Solving -3 + -5x + 12x2 = 136 Solving for variable 'x'. Reorder the terms: -3 + -136 + -5x + 12x2 = 136 + -136 Combine like terms: -3 + -136 = -139 -139 + -5x + 12x2 = 136 + -136 Combine like terms: 136 + -136 = 0 -139 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -11.58333333 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '11.58333333' to each side of the equation. -11.58333333 + -0.4166666667x + 11.58333333 + x2 = 0 + 11.58333333 Reorder the terms: -11.58333333 + 11.58333333 + -0.4166666667x + x2 = 0 + 11.58333333 Combine like terms: -11.58333333 + 11.58333333 = 0.00000000 0.00000000 + -0.4166666667x + x2 = 0 + 11.58333333 -0.4166666667x + x2 = 0 + 11.58333333 Combine like terms: 0 + 11.58333333 = 11.58333333 -0.4166666667x + x2 = 11.58333333 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 = 11.58333333 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 11.58333333 + 0.04340277781 Combine like terms: 11.58333333 + 0.04340277781 = 11.62673610781 0.04340277781 + -0.4166666667x + x2 = 11.62673610781 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 11.62673610781 Calculate the square root of the right side: 3.40980001 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 3.40980001 and -3.40980001.Subproblem 1
x + -0.2083333334 = 3.40980001 Simplifying x + -0.2083333334 = 3.40980001 Reorder the terms: -0.2083333334 + x = 3.40980001 Solving -0.2083333334 + x = 3.40980001 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 = 3.40980001 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 3.40980001 + 0.2083333334 x = 3.40980001 + 0.2083333334 Combine like terms: 3.40980001 + 0.2083333334 = 3.6181333434 x = 3.6181333434 Simplifying x = 3.6181333434Subproblem 2
x + -0.2083333334 = -3.40980001 Simplifying x + -0.2083333334 = -3.40980001 Reorder the terms: -0.2083333334 + x = -3.40980001 Solving -0.2083333334 + x = -3.40980001 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 = -3.40980001 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -3.40980001 + 0.2083333334 x = -3.40980001 + 0.2083333334 Combine like terms: -3.40980001 + 0.2083333334 = -3.2014666766 x = -3.2014666766 Simplifying x = -3.2014666766Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6181333434, -3.2014666766}
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