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Simplifying 2x(3x + 6) = 2x + 17 Reorder the terms: 2x(6 + 3x) = 2x + 17 (6 * 2x + 3x * 2x) = 2x + 17 (12x + 6x2) = 2x + 17 Reorder the terms: 12x + 6x2 = 17 + 2x Solving 12x + 6x2 = 17 + 2x Solving for variable 'x'. Reorder the terms: -17 + 12x + -2x + 6x2 = 17 + 2x + -17 + -2x Combine like terms: 12x + -2x = 10x -17 + 10x + 6x2 = 17 + 2x + -17 + -2x Reorder the terms: -17 + 10x + 6x2 = 17 + -17 + 2x + -2x Combine like terms: 17 + -17 = 0 -17 + 10x + 6x2 = 0 + 2x + -2x -17 + 10x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -17 + 10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.833333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + 1.666666667x + 2.833333333 + x2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + 1.666666667x + x2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 2.833333333 1.666666667x + x2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 1.666666667x + x2 = 2.833333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 2.833333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 2.833333333 + 0.6944444447 Combine like terms: 2.833333333 + 0.6944444447 = 3.5277777777 0.6944444447 + 1.666666667x + x2 = 3.5277777777 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 3.5277777777 Calculate the square root of the right side: 1.878237945 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.878237945 and -1.878237945.Subproblem 1
x + 0.8333333335 = 1.878237945 Simplifying x + 0.8333333335 = 1.878237945 Reorder the terms: 0.8333333335 + x = 1.878237945 Solving 0.8333333335 + x = 1.878237945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.878237945 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.878237945 + -0.8333333335 x = 1.878237945 + -0.8333333335 Combine like terms: 1.878237945 + -0.8333333335 = 1.0449046115 x = 1.0449046115 Simplifying x = 1.0449046115Subproblem 2
x + 0.8333333335 = -1.878237945 Simplifying x + 0.8333333335 = -1.878237945 Reorder the terms: 0.8333333335 + x = -1.878237945 Solving 0.8333333335 + x = -1.878237945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.878237945 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.878237945 + -0.8333333335 x = -1.878237945 + -0.8333333335 Combine like terms: -1.878237945 + -0.8333333335 = -2.7115712785 x = -2.7115712785 Simplifying x = -2.7115712785Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0449046115, -2.7115712785}
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