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Simplifying 9x(x + 3) = 4x + -3 Reorder the terms: 9x(3 + x) = 4x + -3 (3 * 9x + x * 9x) = 4x + -3 (27x + 9x2) = 4x + -3 Reorder the terms: 27x + 9x2 = -3 + 4x Solving 27x + 9x2 = -3 + 4x Solving for variable 'x'. Reorder the terms: 3 + 27x + -4x + 9x2 = -3 + 4x + 3 + -4x Combine like terms: 27x + -4x = 23x 3 + 23x + 9x2 = -3 + 4x + 3 + -4x Reorder the terms: 3 + 23x + 9x2 = -3 + 3 + 4x + -4x Combine like terms: -3 + 3 = 0 3 + 23x + 9x2 = 0 + 4x + -4x 3 + 23x + 9x2 = 4x + -4x Combine like terms: 4x + -4x = 0 3 + 23x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + 2.555555556x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 2.555555556x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 2.555555556x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 2.555555556x + x2 = 0 + -0.3333333333 2.555555556x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 2.555555556x + x2 = -0.3333333333 The x term is 2.555555556x. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556x + 1.632716050 + x2 = -0.3333333333 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556x + x2 = -0.3333333333 + 1.632716050 Combine like terms: -0.3333333333 + 1.632716050 = 1.2993827167 1.632716050 + 2.555555556x + x2 = 1.2993827167 Factor a perfect square on the left side: (x + 1.277777778)(x + 1.277777778) = 1.2993827167 Calculate the square root of the right side: 1.139904696 Break this problem into two subproblems by setting (x + 1.277777778) equal to 1.139904696 and -1.139904696.Subproblem 1
x + 1.277777778 = 1.139904696 Simplifying x + 1.277777778 = 1.139904696 Reorder the terms: 1.277777778 + x = 1.139904696 Solving 1.277777778 + x = 1.139904696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = 1.139904696 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = 1.139904696 + -1.277777778 x = 1.139904696 + -1.277777778 Combine like terms: 1.139904696 + -1.277777778 = -0.137873082 x = -0.137873082 Simplifying x = -0.137873082Subproblem 2
x + 1.277777778 = -1.139904696 Simplifying x + 1.277777778 = -1.139904696 Reorder the terms: 1.277777778 + x = -1.139904696 Solving 1.277777778 + x = -1.139904696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = -1.139904696 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = -1.139904696 + -1.277777778 x = -1.139904696 + -1.277777778 Combine like terms: -1.139904696 + -1.277777778 = -2.417682474 x = -2.417682474 Simplifying x = -2.417682474Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.137873082, -2.417682474}
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