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Simplifying 2x + -5(x + 4) = (x + 1)(x + -3) Reorder the terms: 2x + -5(4 + x) = (x + 1)(x + -3) 2x + (4 * -5 + x * -5) = (x + 1)(x + -3) 2x + (-20 + -5x) = (x + 1)(x + -3) Reorder the terms: -20 + 2x + -5x = (x + 1)(x + -3) Combine like terms: 2x + -5x = -3x -20 + -3x = (x + 1)(x + -3) Reorder the terms: -20 + -3x = (1 + x)(x + -3) Reorder the terms: -20 + -3x = (1 + x)(-3 + x) Multiply (1 + x) * (-3 + x) -20 + -3x = (1(-3 + x) + x(-3 + x)) -20 + -3x = ((-3 * 1 + x * 1) + x(-3 + x)) -20 + -3x = ((-3 + 1x) + x(-3 + x)) -20 + -3x = (-3 + 1x + (-3 * x + x * x)) -20 + -3x = (-3 + 1x + (-3x + x2)) Combine like terms: 1x + -3x = -2x -20 + -3x = (-3 + -2x + x2) Solving -20 + -3x = -3 + -2x + x2 Solving for variable 'x'. Reorder the terms: -20 + 3 + -3x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: -20 + 3 = -17 -17 + -3x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: -3x + 2x = -1x -17 + -1x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Reorder the terms: -17 + -1x + -1x2 = -3 + 3 + -2x + 2x + x2 + -1x2 Combine like terms: -3 + 3 = 0 -17 + -1x + -1x2 = 0 + -2x + 2x + x2 + -1x2 -17 + -1x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 -17 + -1x + -1x2 = 0 + x2 + -1x2 -17 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -17 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + x + x2)' equal to zero and attempt to solve: Simplifying 17 + x + x2 = 0 Solving 17 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x + x2 = 0 + -17 x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 x + x2 = -17 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -17 + 0.25 Reorder the terms: 0.25 + x + x2 = -17 + 0.25 Combine like terms: -17 + 0.25 = -16.75 0.25 + x + x2 = -16.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -16.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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