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Simplifying 3(x + 7) * 12x = 3 + 2x Reorder the terms: 3(7 + x) * 12x = 3 + 2x Reorder the terms for easier multiplication: 3 * 12x(7 + x) = 3 + 2x Multiply 3 * 12 36x(7 + x) = 3 + 2x (7 * 36x + x * 36x) = 3 + 2x (252x + 36x2) = 3 + 2x Solving 252x + 36x2 = 3 + 2x Solving for variable 'x'. Reorder the terms: -3 + 252x + -2x + 36x2 = 3 + 2x + -3 + -2x Combine like terms: 252x + -2x = 250x -3 + 250x + 36x2 = 3 + 2x + -3 + -2x Reorder the terms: -3 + 250x + 36x2 = 3 + -3 + 2x + -2x Combine like terms: 3 + -3 = 0 -3 + 250x + 36x2 = 0 + 2x + -2x -3 + 250x + 36x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -3 + 250x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.08333333333 + 6.944444444x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 6.944444444x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 6.944444444x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 6.944444444x + x2 = 0 + 0.08333333333 6.944444444x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 6.944444444x + x2 = 0.08333333333 The x term is 6.944444444x. Take half its coefficient (3.472222222). Square it (12.05632716) and add it to both sides. Add '12.05632716' to each side of the equation. 6.944444444x + 12.05632716 + x2 = 0.08333333333 + 12.05632716 Reorder the terms: 12.05632716 + 6.944444444x + x2 = 0.08333333333 + 12.05632716 Combine like terms: 0.08333333333 + 12.05632716 = 12.13966049333 12.05632716 + 6.944444444x + x2 = 12.13966049333 Factor a perfect square on the left side: (x + 3.472222222)(x + 3.472222222) = 12.13966049333 Calculate the square root of the right side: 3.484201558 Break this problem into two subproblems by setting (x + 3.472222222) equal to 3.484201558 and -3.484201558.Subproblem 1
x + 3.472222222 = 3.484201558 Simplifying x + 3.472222222 = 3.484201558 Reorder the terms: 3.472222222 + x = 3.484201558 Solving 3.472222222 + x = 3.484201558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.472222222' to each side of the equation. 3.472222222 + -3.472222222 + x = 3.484201558 + -3.472222222 Combine like terms: 3.472222222 + -3.472222222 = 0.000000000 0.000000000 + x = 3.484201558 + -3.472222222 x = 3.484201558 + -3.472222222 Combine like terms: 3.484201558 + -3.472222222 = 0.011979336 x = 0.011979336 Simplifying x = 0.011979336Subproblem 2
x + 3.472222222 = -3.484201558 Simplifying x + 3.472222222 = -3.484201558 Reorder the terms: 3.472222222 + x = -3.484201558 Solving 3.472222222 + x = -3.484201558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.472222222' to each side of the equation. 3.472222222 + -3.472222222 + x = -3.484201558 + -3.472222222 Combine like terms: 3.472222222 + -3.472222222 = 0.000000000 0.000000000 + x = -3.484201558 + -3.472222222 x = -3.484201558 + -3.472222222 Combine like terms: -3.484201558 + -3.472222222 = -6.95642378 x = -6.95642378 Simplifying x = -6.95642378Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.011979336, -6.95642378}
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