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Simplifying 2x2 + 1 = (x + 1)(x + 2) Reorder the terms: 1 + 2x2 = (x + 1)(x + 2) Reorder the terms: 1 + 2x2 = (1 + x)(x + 2) Reorder the terms: 1 + 2x2 = (1 + x)(2 + x) Multiply (1 + x) * (2 + x) 1 + 2x2 = (1(2 + x) + x(2 + x)) 1 + 2x2 = ((2 * 1 + x * 1) + x(2 + x)) 1 + 2x2 = ((2 + 1x) + x(2 + x)) 1 + 2x2 = (2 + 1x + (2 * x + x * x)) 1 + 2x2 = (2 + 1x + (2x + x2)) Combine like terms: 1x + 2x = 3x 1 + 2x2 = (2 + 3x + x2) Solving 1 + 2x2 = 2 + 3x + x2 Solving for variable 'x'. Reorder the terms: 1 + -2 + -3x + 2x2 + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Combine like terms: 1 + -2 = -1 -1 + -3x + 2x2 + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -1 + -3x + 1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Reorder the terms: -1 + -3x + 1x2 = 2 + -2 + 3x + -3x + x2 + -1x2 Combine like terms: 2 + -2 = 0 -1 + -3x + 1x2 = 0 + 3x + -3x + x2 + -1x2 -1 + -3x + 1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -1 + -3x + 1x2 = 0 + x2 + -1x2 -1 + -3x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + -3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -3x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x + x2 = 0 + 1 -3x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3x + x2 = 1 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 1 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + -3x + x2 = 3.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -1.5 = 1.802775638 Simplifying x + -1.5 = 1.802775638 Reorder the terms: -1.5 + x = 1.802775638 Solving -1.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.802775638 + 1.5 x = 1.802775638 + 1.5 Combine like terms: 1.802775638 + 1.5 = 3.302775638 x = 3.302775638 Simplifying x = 3.302775638Subproblem 2
x + -1.5 = -1.802775638 Simplifying x + -1.5 = -1.802775638 Reorder the terms: -1.5 + x = -1.802775638 Solving -1.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.802775638 + 1.5 x = -1.802775638 + 1.5 Combine like terms: -1.802775638 + 1.5 = -0.302775638 x = -0.302775638 Simplifying x = -0.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.302775638, -0.302775638}
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