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Simplifying 3x(2x + 1) = 2x + 11 Reorder the terms: 3x(1 + 2x) = 2x + 11 (1 * 3x + 2x * 3x) = 2x + 11 (3x + 6x2) = 2x + 11 Reorder the terms: 3x + 6x2 = 11 + 2x Solving 3x + 6x2 = 11 + 2x Solving for variable 'x'. Reorder the terms: -11 + 3x + -2x + 6x2 = 11 + 2x + -11 + -2x Combine like terms: 3x + -2x = 1x -11 + 1x + 6x2 = 11 + 2x + -11 + -2x Reorder the terms: -11 + 1x + 6x2 = 11 + -11 + 2x + -2x Combine like terms: 11 + -11 = 0 -11 + 1x + 6x2 = 0 + 2x + -2x -11 + 1x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -11 + 1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 0.1666666667x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 0.1666666667x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 1.833333333 0.1666666667x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 0.1666666667x + x2 = 1.833333333 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 1.833333333 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 1.833333333 + 0.006944444447 Combine like terms: 1.833333333 + 0.006944444447 = 1.840277777447 0.006944444447 + 0.1666666667x + x2 = 1.840277777447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 1.840277777447 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 1.356568383 and -1.356568383.Subproblem 1
x + 0.08333333335 = 1.356568383 Simplifying x + 0.08333333335 = 1.356568383 Reorder the terms: 0.08333333335 + x = 1.356568383 Solving 0.08333333335 + x = 1.356568383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 1.356568383 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.356568383 + -0.08333333335 x = 1.356568383 + -0.08333333335 Combine like terms: 1.356568383 + -0.08333333335 = 1.27323504965 x = 1.27323504965 Simplifying x = 1.27323504965Subproblem 2
x + 0.08333333335 = -1.356568383 Simplifying x + 0.08333333335 = -1.356568383 Reorder the terms: 0.08333333335 + x = -1.356568383 Solving 0.08333333335 + x = -1.356568383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -1.356568383 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.356568383 + -0.08333333335 x = -1.356568383 + -0.08333333335 Combine like terms: -1.356568383 + -0.08333333335 = -1.43990171635 x = -1.43990171635 Simplifying x = -1.43990171635Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.27323504965, -1.43990171635}
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