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Simplifying 2(x + 1)(x + -3) + -1x + 1x + 1 = 0 Reorder the terms: 2(1 + x)(x + -3) + -1x + 1x + 1 = 0 Reorder the terms: 2(1 + x)(-3 + x) + -1x + 1x + 1 = 0 Multiply (1 + x) * (-3 + x) 2(1(-3 + x) + x(-3 + x)) + -1x + 1x + 1 = 0 2((-3 * 1 + x * 1) + x(-3 + x)) + -1x + 1x + 1 = 0 2((-3 + 1x) + x(-3 + x)) + -1x + 1x + 1 = 0 2(-3 + 1x + (-3 * x + x * x)) + -1x + 1x + 1 = 0 2(-3 + 1x + (-3x + x2)) + -1x + 1x + 1 = 0 Combine like terms: 1x + -3x = -2x 2(-3 + -2x + x2) + -1x + 1x + 1 = 0 (-3 * 2 + -2x * 2 + x2 * 2) + -1x + 1x + 1 = 0 (-6 + -4x + 2x2) + -1x + 1x + 1 = 0 Reorder the terms: -6 + 1 + -4x + -1x + 1x + 2x2 = 0 Combine like terms: -6 + 1 = -5 -5 + -4x + -1x + 1x + 2x2 = 0 Combine like terms: -4x + -1x = -5x -5 + -5x + 1x + 2x2 = 0 Combine like terms: -5x + 1x = -4x -5 + -4x + 2x2 = 0 Solving -5 + -4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -2x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2x + x2 = 0 + 2.5 -2x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2x + x2 = 2.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 2.5 + 1 Reorder the terms: 1 + -2x + x2 = 2.5 + 1 Combine like terms: 2.5 + 1 = 3.5 1 + -2x + x2 = 3.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + -1) equal to 1.870828693 and -1.870828693.Subproblem 1
x + -1 = 1.870828693 Simplifying x + -1 = 1.870828693 Reorder the terms: -1 + x = 1.870828693 Solving -1 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.870828693 + 1 x = 1.870828693 + 1 Combine like terms: 1.870828693 + 1 = 2.870828693 x = 2.870828693 Simplifying x = 2.870828693Subproblem 2
x + -1 = -1.870828693 Simplifying x + -1 = -1.870828693 Reorder the terms: -1 + x = -1.870828693 Solving -1 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.870828693 + 1 x = -1.870828693 + 1 Combine like terms: -1.870828693 + 1 = -0.870828693 x = -0.870828693 Simplifying x = -0.870828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.870828693, -0.870828693}
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