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Simplifying 2x(x) = x + 12(x + 3) Multiply x * x 2x2 = x + 12(x + 3) Reorder the terms: 2x2 = x + 12(3 + x) 2x2 = x + (3 * 12 + x * 12) 2x2 = x + (36 + 12x) Reorder the terms: 2x2 = 36 + x + 12x Combine like terms: x + 12x = 13x 2x2 = 36 + 13x Solving 2x2 = 36 + 13x Solving for variable 'x'. Reorder the terms: -36 + -13x + 2x2 = 36 + 13x + -36 + -13x Reorder the terms: -36 + -13x + 2x2 = 36 + -36 + 13x + -13x Combine like terms: 36 + -36 = 0 -36 + -13x + 2x2 = 0 + 13x + -13x -36 + -13x + 2x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -36 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + -6.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -6.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -6.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6.5x + x2 = 0 + 18 -6.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6.5x + x2 = 18 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 18 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 18 + 10.5625 Combine like terms: 18 + 10.5625 = 28.5625 10.5625 + -6.5x + x2 = 28.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 28.5625 Calculate the square root of the right side: 5.344389582 Break this problem into two subproblems by setting (x + -3.25) equal to 5.344389582 and -5.344389582.Subproblem 1
x + -3.25 = 5.344389582 Simplifying x + -3.25 = 5.344389582 Reorder the terms: -3.25 + x = 5.344389582 Solving -3.25 + x = 5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 5.344389582 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 5.344389582 + 3.25 x = 5.344389582 + 3.25 Combine like terms: 5.344389582 + 3.25 = 8.594389582 x = 8.594389582 Simplifying x = 8.594389582Subproblem 2
x + -3.25 = -5.344389582 Simplifying x + -3.25 = -5.344389582 Reorder the terms: -3.25 + x = -5.344389582 Solving -3.25 + x = -5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -5.344389582 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -5.344389582 + 3.25 x = -5.344389582 + 3.25 Combine like terms: -5.344389582 + 3.25 = -2.094389582 x = -2.094389582 Simplifying x = -2.094389582Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.594389582, -2.094389582}
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