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Simplifying (3x)(4x + 13) = 139 Remove parenthesis around (3x) 3x(4x + 13) = 139 Reorder the terms: 3x(13 + 4x) = 139 (13 * 3x + 4x * 3x) = 139 (39x + 12x2) = 139 Solving 39x + 12x2 = 139 Solving for variable 'x'. Reorder the terms: -139 + 39x + 12x2 = 139 + -139 Combine like terms: 139 + -139 = 0 -139 + 39x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -11.58333333 + 3.25x + x2 = 0 Move the constant term to the right: Add '11.58333333' to each side of the equation. -11.58333333 + 3.25x + 11.58333333 + x2 = 0 + 11.58333333 Reorder the terms: -11.58333333 + 11.58333333 + 3.25x + x2 = 0 + 11.58333333 Combine like terms: -11.58333333 + 11.58333333 = 0.00000000 0.00000000 + 3.25x + x2 = 0 + 11.58333333 3.25x + x2 = 0 + 11.58333333 Combine like terms: 0 + 11.58333333 = 11.58333333 3.25x + x2 = 11.58333333 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 11.58333333 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 11.58333333 + 2.640625 Combine like terms: 11.58333333 + 2.640625 = 14.22395833 2.640625 + 3.25x + x2 = 14.22395833 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 14.22395833 Calculate the square root of the right side: 3.771466337 Break this problem into two subproblems by setting (x + 1.625) equal to 3.771466337 and -3.771466337.Subproblem 1
x + 1.625 = 3.771466337 Simplifying x + 1.625 = 3.771466337 Reorder the terms: 1.625 + x = 3.771466337 Solving 1.625 + x = 3.771466337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 3.771466337 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 3.771466337 + -1.625 x = 3.771466337 + -1.625 Combine like terms: 3.771466337 + -1.625 = 2.146466337 x = 2.146466337 Simplifying x = 2.146466337Subproblem 2
x + 1.625 = -3.771466337 Simplifying x + 1.625 = -3.771466337 Reorder the terms: 1.625 + x = -3.771466337 Solving 1.625 + x = -3.771466337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -3.771466337 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -3.771466337 + -1.625 x = -3.771466337 + -1.625 Combine like terms: -3.771466337 + -1.625 = -5.396466337 x = -5.396466337 Simplifying x = -5.396466337Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.146466337, -5.396466337}
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