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Simplifying 2x(x + -3) + 12 = 2(x + 1) + -3x + 23 Reorder the terms: 2x(-3 + x) + 12 = 2(x + 1) + -3x + 23 (-3 * 2x + x * 2x) + 12 = 2(x + 1) + -3x + 23 (-6x + 2x2) + 12 = 2(x + 1) + -3x + 23 Reorder the terms: 12 + -6x + 2x2 = 2(x + 1) + -3x + 23 Reorder the terms: 12 + -6x + 2x2 = 2(1 + x) + -3x + 23 12 + -6x + 2x2 = (1 * 2 + x * 2) + -3x + 23 12 + -6x + 2x2 = (2 + 2x) + -3x + 23 Reorder the terms: 12 + -6x + 2x2 = 2 + 23 + 2x + -3x Combine like terms: 2 + 23 = 25 12 + -6x + 2x2 = 25 + 2x + -3x Combine like terms: 2x + -3x = -1x 12 + -6x + 2x2 = 25 + -1x Solving 12 + -6x + 2x2 = 25 + -1x Solving for variable 'x'. Reorder the terms: 12 + -25 + -6x + x + 2x2 = 25 + -1x + -25 + x Combine like terms: 12 + -25 = -13 -13 + -6x + x + 2x2 = 25 + -1x + -25 + x Combine like terms: -6x + x = -5x -13 + -5x + 2x2 = 25 + -1x + -25 + x Reorder the terms: -13 + -5x + 2x2 = 25 + -25 + -1x + x Combine like terms: 25 + -25 = 0 -13 + -5x + 2x2 = 0 + -1x + x -13 + -5x + 2x2 = -1x + x Combine like terms: -1x + x = 0 -13 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -2.5x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -2.5x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -2.5x + x2 = 0 + 6.5 -2.5x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -2.5x + x2 = 6.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 6.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 6.5 + 1.5625 Combine like terms: 6.5 + 1.5625 = 8.0625 1.5625 + -2.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -1.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -1.25 = 2.839454173 Simplifying x + -1.25 = 2.839454173 Reorder the terms: -1.25 + x = 2.839454173 Solving -1.25 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.839454173 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.839454173 + 1.25 x = 2.839454173 + 1.25 Combine like terms: 2.839454173 + 1.25 = 4.089454173 x = 4.089454173 Simplifying x = 4.089454173Subproblem 2
x + -1.25 = -2.839454173 Simplifying x + -1.25 = -2.839454173 Reorder the terms: -1.25 + x = -2.839454173 Solving -1.25 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.839454173 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.839454173 + 1.25 x = -2.839454173 + 1.25 Combine like terms: -2.839454173 + 1.25 = -1.589454173 x = -1.589454173 Simplifying x = -1.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.089454173, -1.589454173}
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