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Simplifying 2x(x + 1) + -3 = 12x + -12 Reorder the terms: 2x(1 + x) + -3 = 12x + -12 (1 * 2x + x * 2x) + -3 = 12x + -12 (2x + 2x2) + -3 = 12x + -12 Reorder the terms: -3 + 2x + 2x2 = 12x + -12 Reorder the terms: -3 + 2x + 2x2 = -12 + 12x Solving -3 + 2x + 2x2 = -12 + 12x Solving for variable 'x'. Reorder the terms: -3 + 12 + 2x + -12x + 2x2 = -12 + 12x + 12 + -12x Combine like terms: -3 + 12 = 9 9 + 2x + -12x + 2x2 = -12 + 12x + 12 + -12x Combine like terms: 2x + -12x = -10x 9 + -10x + 2x2 = -12 + 12x + 12 + -12x Reorder the terms: 9 + -10x + 2x2 = -12 + 12 + 12x + -12x Combine like terms: -12 + 12 = 0 9 + -10x + 2x2 = 0 + 12x + -12x 9 + -10x + 2x2 = 12x + -12x Combine like terms: 12x + -12x = 0 9 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -5x + x2 = 0 + -4.5 -5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -5x + x2 = -4.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.5 + 6.25 Combine like terms: -4.5 + 6.25 = 1.75 6.25 + -5x + x2 = 1.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -2.5) equal to 1.322875656 and -1.322875656.Subproblem 1
x + -2.5 = 1.322875656 Simplifying x + -2.5 = 1.322875656 Reorder the terms: -2.5 + x = 1.322875656 Solving -2.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.322875656 + 2.5 x = 1.322875656 + 2.5 Combine like terms: 1.322875656 + 2.5 = 3.822875656 x = 3.822875656 Simplifying x = 3.822875656Subproblem 2
x + -2.5 = -1.322875656 Simplifying x + -2.5 = -1.322875656 Reorder the terms: -2.5 + x = -1.322875656 Solving -2.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.322875656 + 2.5 x = -1.322875656 + 2.5 Combine like terms: -1.322875656 + 2.5 = 1.177124344 x = 1.177124344 Simplifying x = 1.177124344Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.822875656, 1.177124344}
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