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Simplifying (4x + -1)(3x + 1) = 140 Reorder the terms: (-1 + 4x)(3x + 1) = 140 Reorder the terms: (-1 + 4x)(1 + 3x) = 140 Multiply (-1 + 4x) * (1 + 3x) (-1(1 + 3x) + 4x * (1 + 3x)) = 140 ((1 * -1 + 3x * -1) + 4x * (1 + 3x)) = 140 ((-1 + -3x) + 4x * (1 + 3x)) = 140 (-1 + -3x + (1 * 4x + 3x * 4x)) = 140 (-1 + -3x + (4x + 12x2)) = 140 Combine like terms: -3x + 4x = 1x (-1 + 1x + 12x2) = 140 Solving -1 + 1x + 12x2 = 140 Solving for variable 'x'. Reorder the terms: -1 + -140 + 1x + 12x2 = 140 + -140 Combine like terms: -1 + -140 = -141 -141 + 1x + 12x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -141 + 1x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -11.75 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '11.75' to each side of the equation. -11.75 + 0.08333333333x + 11.75 + x2 = 0 + 11.75 Reorder the terms: -11.75 + 11.75 + 0.08333333333x + x2 = 0 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + 0.08333333333x + x2 = 0 + 11.75 0.08333333333x + x2 = 0 + 11.75 Combine like terms: 0 + 11.75 = 11.75 0.08333333333x + x2 = 11.75 The x term is 0.08333333333x. Take half its coefficient (0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. 0.08333333333x + 0.001736111111 + x2 = 11.75 + 0.001736111111 Reorder the terms: 0.001736111111 + 0.08333333333x + x2 = 11.75 + 0.001736111111 Combine like terms: 11.75 + 0.001736111111 = 11.751736111111 0.001736111111 + 0.08333333333x + x2 = 11.751736111111 Factor a perfect square on the left side: (x + 0.04166666667)(x + 0.04166666667) = 11.751736111111 Calculate the square root of the right side: 3.428080529 Break this problem into two subproblems by setting (x + 0.04166666667) equal to 3.428080529 and -3.428080529.Subproblem 1
x + 0.04166666667 = 3.428080529 Simplifying x + 0.04166666667 = 3.428080529 Reorder the terms: 0.04166666667 + x = 3.428080529 Solving 0.04166666667 + x = 3.428080529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + x = 3.428080529 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = 3.428080529 + -0.04166666667 x = 3.428080529 + -0.04166666667 Combine like terms: 3.428080529 + -0.04166666667 = 3.38641386233 x = 3.38641386233 Simplifying x = 3.38641386233Subproblem 2
x + 0.04166666667 = -3.428080529 Simplifying x + 0.04166666667 = -3.428080529 Reorder the terms: 0.04166666667 + x = -3.428080529 Solving 0.04166666667 + x = -3.428080529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + x = -3.428080529 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = -3.428080529 + -0.04166666667 x = -3.428080529 + -0.04166666667 Combine like terms: -3.428080529 + -0.04166666667 = -3.46974719567 x = -3.46974719567 Simplifying x = -3.46974719567Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.38641386233, -3.46974719567}
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