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Simplifying (x + 39)(3x + 20) = x Reorder the terms: (39 + x)(3x + 20) = x Reorder the terms: (39 + x)(20 + 3x) = x Multiply (39 + x) * (20 + 3x) (39(20 + 3x) + x(20 + 3x)) = x ((20 * 39 + 3x * 39) + x(20 + 3x)) = x ((780 + 117x) + x(20 + 3x)) = x (780 + 117x + (20 * x + 3x * x)) = x (780 + 117x + (20x + 3x2)) = x Combine like terms: 117x + 20x = 137x (780 + 137x + 3x2) = x Solving 780 + 137x + 3x2 = x Solving for variable 'x'. Reorder the terms: 780 + 137x + -1x + 3x2 = x + -1x Combine like terms: 137x + -1x = 136x 780 + 136x + 3x2 = x + -1x Combine like terms: x + -1x = 0 780 + 136x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 260 + 45.33333333x + x2 = 0 Move the constant term to the right: Add '-260' to each side of the equation. 260 + 45.33333333x + -260 + x2 = 0 + -260 Reorder the terms: 260 + -260 + 45.33333333x + x2 = 0 + -260 Combine like terms: 260 + -260 = 0 0 + 45.33333333x + x2 = 0 + -260 45.33333333x + x2 = 0 + -260 Combine like terms: 0 + -260 = -260 45.33333333x + x2 = -260 The x term is 45.33333333x. Take half its coefficient (22.66666667). Square it (513.7777779) and add it to both sides. Add '513.7777779' to each side of the equation. 45.33333333x + 513.7777779 + x2 = -260 + 513.7777779 Reorder the terms: 513.7777779 + 45.33333333x + x2 = -260 + 513.7777779 Combine like terms: -260 + 513.7777779 = 253.7777779 513.7777779 + 45.33333333x + x2 = 253.7777779 Factor a perfect square on the left side: (x + 22.66666667)(x + 22.66666667) = 253.7777779 Calculate the square root of the right side: 15.930404198 Break this problem into two subproblems by setting (x + 22.66666667) equal to 15.930404198 and -15.930404198.Subproblem 1
x + 22.66666667 = 15.930404198 Simplifying x + 22.66666667 = 15.930404198 Reorder the terms: 22.66666667 + x = 15.930404198 Solving 22.66666667 + x = 15.930404198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.66666667' to each side of the equation. 22.66666667 + -22.66666667 + x = 15.930404198 + -22.66666667 Combine like terms: 22.66666667 + -22.66666667 = 0.00000000 0.00000000 + x = 15.930404198 + -22.66666667 x = 15.930404198 + -22.66666667 Combine like terms: 15.930404198 + -22.66666667 = -6.736262472 x = -6.736262472 Simplifying x = -6.736262472Subproblem 2
x + 22.66666667 = -15.930404198 Simplifying x + 22.66666667 = -15.930404198 Reorder the terms: 22.66666667 + x = -15.930404198 Solving 22.66666667 + x = -15.930404198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.66666667' to each side of the equation. 22.66666667 + -22.66666667 + x = -15.930404198 + -22.66666667 Combine like terms: 22.66666667 + -22.66666667 = 0.00000000 0.00000000 + x = -15.930404198 + -22.66666667 x = -15.930404198 + -22.66666667 Combine like terms: -15.930404198 + -22.66666667 = -38.597070868 x = -38.597070868 Simplifying x = -38.597070868Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.736262472, -38.597070868}
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