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Simplifying (9x + -1)(2x + 1) + -6 = 0 Reorder the terms: (-1 + 9x)(2x + 1) + -6 = 0 Reorder the terms: (-1 + 9x)(1 + 2x) + -6 = 0 Multiply (-1 + 9x) * (1 + 2x) (-1(1 + 2x) + 9x * (1 + 2x)) + -6 = 0 ((1 * -1 + 2x * -1) + 9x * (1 + 2x)) + -6 = 0 ((-1 + -2x) + 9x * (1 + 2x)) + -6 = 0 (-1 + -2x + (1 * 9x + 2x * 9x)) + -6 = 0 (-1 + -2x + (9x + 18x2)) + -6 = 0 Combine like terms: -2x + 9x = 7x (-1 + 7x + 18x2) + -6 = 0 Reorder the terms: -1 + -6 + 7x + 18x2 = 0 Combine like terms: -1 + -6 = -7 -7 + 7x + 18x2 = 0 Solving -7 + 7x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3888888889 + 0.3888888889x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + 0.3888888889x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + 0.3888888889x + x2 = 0 + 0.3888888889 0.3888888889x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 0.3888888889x + x2 = 0.3888888889 The x term is 0.3888888889x. Take half its coefficient (0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. 0.3888888889x + 0.03780864200 + x2 = 0.3888888889 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889x + x2 = 0.3888888889 + 0.03780864200 Combine like terms: 0.3888888889 + 0.03780864200 = 0.4266975309 0.03780864200 + 0.3888888889x + x2 = 0.4266975309 Factor a perfect square on the left side: (x + 0.1944444445)(x + 0.1944444445) = 0.4266975309 Calculate the square root of the right side: 0.65322089 Break this problem into two subproblems by setting (x + 0.1944444445) equal to 0.65322089 and -0.65322089.Subproblem 1
x + 0.1944444445 = 0.65322089 Simplifying x + 0.1944444445 = 0.65322089 Reorder the terms: 0.1944444445 + x = 0.65322089 Solving 0.1944444445 + x = 0.65322089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1944444445' to each side of the equation. 0.1944444445 + -0.1944444445 + x = 0.65322089 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = 0.65322089 + -0.1944444445 x = 0.65322089 + -0.1944444445 Combine like terms: 0.65322089 + -0.1944444445 = 0.4587764455 x = 0.4587764455 Simplifying x = 0.4587764455Subproblem 2
x + 0.1944444445 = -0.65322089 Simplifying x + 0.1944444445 = -0.65322089 Reorder the terms: 0.1944444445 + x = -0.65322089 Solving 0.1944444445 + x = -0.65322089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1944444445' to each side of the equation. 0.1944444445 + -0.1944444445 + x = -0.65322089 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = -0.65322089 + -0.1944444445 x = -0.65322089 + -0.1944444445 Combine like terms: -0.65322089 + -0.1944444445 = -0.8476653345 x = -0.8476653345 Simplifying x = -0.8476653345Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4587764455, -0.8476653345}
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