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Simplifying 2x(x + -3) + -5x = 2x + 3(1 + -2x) Reorder the terms: 2x(-3 + x) + -5x = 2x + 3(1 + -2x) (-3 * 2x + x * 2x) + -5x = 2x + 3(1 + -2x) (-6x + 2x2) + -5x = 2x + 3(1 + -2x) Reorder the terms: -6x + -5x + 2x2 = 2x + 3(1 + -2x) Combine like terms: -6x + -5x = -11x -11x + 2x2 = 2x + 3(1 + -2x) -11x + 2x2 = 2x + (1 * 3 + -2x * 3) -11x + 2x2 = 2x + (3 + -6x) Reorder the terms: -11x + 2x2 = 3 + 2x + -6x Combine like terms: 2x + -6x = -4x -11x + 2x2 = 3 + -4x Solving -11x + 2x2 = 3 + -4x Solving for variable 'x'. Reorder the terms: -3 + -11x + 4x + 2x2 = 3 + -4x + -3 + 4x Combine like terms: -11x + 4x = -7x -3 + -7x + 2x2 = 3 + -4x + -3 + 4x Reorder the terms: -3 + -7x + 2x2 = 3 + -3 + -4x + 4x Combine like terms: 3 + -3 = 0 -3 + -7x + 2x2 = 0 + -4x + 4x -3 + -7x + 2x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -3 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3.5x + x2 = 0 + 1.5 -3.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3.5x + x2 = 1.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 1.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 1.5 + 3.0625 Combine like terms: 1.5 + 3.0625 = 4.5625 3.0625 + -3.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -1.75) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -1.75 = 2.136000936 Simplifying x + -1.75 = 2.136000936 Reorder the terms: -1.75 + x = 2.136000936 Solving -1.75 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.136000936 + 1.75 x = 2.136000936 + 1.75 Combine like terms: 2.136000936 + 1.75 = 3.886000936 x = 3.886000936 Simplifying x = 3.886000936Subproblem 2
x + -1.75 = -2.136000936 Simplifying x + -1.75 = -2.136000936 Reorder the terms: -1.75 + x = -2.136000936 Solving -1.75 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.136000936 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.136000936 + 1.75 x = -2.136000936 + 1.75 Combine like terms: -2.136000936 + 1.75 = -0.386000936 x = -0.386000936 Simplifying x = -0.386000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.886000936, -0.386000936}
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