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Simplifying (3x + 2)(x + -1) = x(x + 5) Reorder the terms: (2 + 3x)(x + -1) = x(x + 5) Reorder the terms: (2 + 3x)(-1 + x) = x(x + 5) Multiply (2 + 3x) * (-1 + x) (2(-1 + x) + 3x * (-1 + x)) = x(x + 5) ((-1 * 2 + x * 2) + 3x * (-1 + x)) = x(x + 5) ((-2 + 2x) + 3x * (-1 + x)) = x(x + 5) (-2 + 2x + (-1 * 3x + x * 3x)) = x(x + 5) (-2 + 2x + (-3x + 3x2)) = x(x + 5) Combine like terms: 2x + -3x = -1x (-2 + -1x + 3x2) = x(x + 5) Reorder the terms: -2 + -1x + 3x2 = x(5 + x) -2 + -1x + 3x2 = (5 * x + x * x) -2 + -1x + 3x2 = (5x + x2) Solving -2 + -1x + 3x2 = 5x + x2 Solving for variable 'x'. Reorder the terms: -2 + -1x + -5x + 3x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: -1x + -5x = -6x -2 + -6x + 3x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -2 + -6x + 2x2 = 5x + x2 + -5x + -1x2 Reorder the terms: -2 + -6x + 2x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 -2 + -6x + 2x2 = 0 + x2 + -1x2 -2 + -6x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -3x + x2)' equal to zero and attempt to solve: Simplifying -1 + -3x + x2 = 0 Solving -1 + -3x + x2 = 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}Solution
x = {3.302775638, -0.302775638}
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