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Simplifying 3x(2x + 1) = 17 Reorder the terms: 3x(1 + 2x) = 17 (1 * 3x + 2x * 3x) = 17 (3x + 6x2) = 17 Solving 3x + 6x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 3x + 6x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.833333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + 0.5x + 2.833333333 + x2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + 0.5x + x2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 2.833333333 0.5x + x2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 0.5x + x2 = 2.833333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 2.833333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2.833333333 + 0.0625 Combine like terms: 2.833333333 + 0.0625 = 2.895833333 0.0625 + 0.5x + x2 = 2.895833333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.895833333 Calculate the square root of the right side: 1.701714821 Break this problem into two subproblems by setting (x + 0.25) equal to 1.701714821 and -1.701714821.Subproblem 1
x + 0.25 = 1.701714821 Simplifying x + 0.25 = 1.701714821 Reorder the terms: 0.25 + x = 1.701714821 Solving 0.25 + x = 1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.701714821 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.701714821 + -0.25 x = 1.701714821 + -0.25 Combine like terms: 1.701714821 + -0.25 = 1.451714821 x = 1.451714821 Simplifying x = 1.451714821Subproblem 2
x + 0.25 = -1.701714821 Simplifying x + 0.25 = -1.701714821 Reorder the terms: 0.25 + x = -1.701714821 Solving 0.25 + x = -1.701714821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.701714821 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.701714821 + -0.25 x = -1.701714821 + -0.25 Combine like terms: -1.701714821 + -0.25 = -1.951714821 x = -1.951714821 Simplifying x = -1.951714821Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.451714821, -1.951714821}
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