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Simplifying 2x(x + -3) + 5 = 3(x + -1) Reorder the terms: 2x(-3 + x) + 5 = 3(x + -1) (-3 * 2x + x * 2x) + 5 = 3(x + -1) (-6x + 2x2) + 5 = 3(x + -1) Reorder the terms: 5 + -6x + 2x2 = 3(x + -1) Reorder the terms: 5 + -6x + 2x2 = 3(-1 + x) 5 + -6x + 2x2 = (-1 * 3 + x * 3) 5 + -6x + 2x2 = (-3 + 3x) Solving 5 + -6x + 2x2 = -3 + 3x Solving for variable 'x'. Reorder the terms: 5 + 3 + -6x + -3x + 2x2 = -3 + 3x + 3 + -3x Combine like terms: 5 + 3 = 8 8 + -6x + -3x + 2x2 = -3 + 3x + 3 + -3x Combine like terms: -6x + -3x = -9x 8 + -9x + 2x2 = -3 + 3x + 3 + -3x Reorder the terms: 8 + -9x + 2x2 = -3 + 3 + 3x + -3x Combine like terms: -3 + 3 = 0 8 + -9x + 2x2 = 0 + 3x + -3x 8 + -9x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 8 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -4.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -4.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.5x + x2 = 0 + -4 -4.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.5x + x2 = -4 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -4 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -4 + 5.0625 Combine like terms: -4 + 5.0625 = 1.0625 5.0625 + -4.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -2.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + -2.25 = 1.030776406 Simplifying x + -2.25 = 1.030776406 Reorder the terms: -2.25 + x = 1.030776406 Solving -2.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.030776406 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.030776406 + 2.25 x = 1.030776406 + 2.25 Combine like terms: 1.030776406 + 2.25 = 3.280776406 x = 3.280776406 Simplifying x = 3.280776406Subproblem 2
x + -2.25 = -1.030776406 Simplifying x + -2.25 = -1.030776406 Reorder the terms: -2.25 + x = -1.030776406 Solving -2.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.030776406 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.030776406 + 2.25 x = -1.030776406 + 2.25 Combine like terms: -1.030776406 + 2.25 = 1.219223594 x = 1.219223594 Simplifying x = 1.219223594Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.280776406, 1.219223594}
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