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Simplifying (2 + -1x)(5x + 3) = (-5 + 1)(4 + x) Reorder the terms: (2 + -1x)(3 + 5x) = (-5 + 1)(4 + x) Multiply (2 + -1x) * (3 + 5x) (2(3 + 5x) + -1x * (3 + 5x)) = (-5 + 1)(4 + x) ((3 * 2 + 5x * 2) + -1x * (3 + 5x)) = (-5 + 1)(4 + x) ((6 + 10x) + -1x * (3 + 5x)) = (-5 + 1)(4 + x) (6 + 10x + (3 * -1x + 5x * -1x)) = (-5 + 1)(4 + x) (6 + 10x + (-3x + -5x2)) = (-5 + 1)(4 + x) Combine like terms: 10x + -3x = 7x (6 + 7x + -5x2) = (-5 + 1)(4 + x) Combine like terms: -5 + 1 = -4 6 + 7x + -5x2 = (-4)(4 + x) 6 + 7x + -5x2 = (4 * -4 + x * -4) 6 + 7x + -5x2 = (-16 + -4x) Solving 6 + 7x + -5x2 = -16 + -4x Solving for variable 'x'. Reorder the terms: 6 + 16 + 7x + 4x + -5x2 = -16 + -4x + 16 + 4x Combine like terms: 6 + 16 = 22 22 + 7x + 4x + -5x2 = -16 + -4x + 16 + 4x Combine like terms: 7x + 4x = 11x 22 + 11x + -5x2 = -16 + -4x + 16 + 4x Reorder the terms: 22 + 11x + -5x2 = -16 + 16 + -4x + 4x Combine like terms: -16 + 16 = 0 22 + 11x + -5x2 = 0 + -4x + 4x 22 + 11x + -5x2 = -4x + 4x Combine like terms: -4x + 4x = 0 22 + 11x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.4 + -2.2x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + -2.2x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + -2.2x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + -2.2x + x2 = 0 + 4.4 -2.2x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 -2.2x + x2 = 4.4 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 4.4 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 4.4 + 1.21 Combine like terms: 4.4 + 1.21 = 5.61 1.21 + -2.2x + x2 = 5.61 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 5.61 Calculate the square root of the right side: 2.368543856 Break this problem into two subproblems by setting (x + -1.1) equal to 2.368543856 and -2.368543856.Subproblem 1
x + -1.1 = 2.368543856 Simplifying x + -1.1 = 2.368543856 Reorder the terms: -1.1 + x = 2.368543856 Solving -1.1 + x = 2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 2.368543856 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 2.368543856 + 1.1 x = 2.368543856 + 1.1 Combine like terms: 2.368543856 + 1.1 = 3.468543856 x = 3.468543856 Simplifying x = 3.468543856Subproblem 2
x + -1.1 = -2.368543856 Simplifying x + -1.1 = -2.368543856 Reorder the terms: -1.1 + x = -2.368543856 Solving -1.1 + x = -2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -2.368543856 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -2.368543856 + 1.1 x = -2.368543856 + 1.1 Combine like terms: -2.368543856 + 1.1 = -1.268543856 x = -1.268543856 Simplifying x = -1.268543856Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.468543856, -1.268543856}
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