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Simplifying 0.5(6x + 4) = (x + 3)(x + 1) Reorder the terms: 0.5(4 + 6x) = (x + 3)(x + 1) (4 * 0.5 + 6x * 0.5) = (x + 3)(x + 1) (2 + 3x) = (x + 3)(x + 1) Reorder the terms: 2 + 3x = (3 + x)(x + 1) Reorder the terms: 2 + 3x = (3 + x)(1 + x) Multiply (3 + x) * (1 + x) 2 + 3x = (3(1 + x) + x(1 + x)) 2 + 3x = ((1 * 3 + x * 3) + x(1 + x)) 2 + 3x = ((3 + 3x) + x(1 + x)) 2 + 3x = (3 + 3x + (1 * x + x * x)) 2 + 3x = (3 + 3x + (1x + x2)) Combine like terms: 3x + 1x = 4x 2 + 3x = (3 + 4x + x2) Solving 2 + 3x = 3 + 4x + x2 Solving for variable 'x'. Reorder the terms: 2 + -3 + 3x + -4x + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Combine like terms: 2 + -3 = -1 -1 + 3x + -4x + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Combine like terms: 3x + -4x = -1x -1 + -1x + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Reorder the terms: -1 + -1x + -1x2 = 3 + -3 + 4x + -4x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -1 + -1x + -1x2 = 0 + 4x + -4x + x2 + -1x2 -1 + -1x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -1 + -1x + -1x2 = 0 + x2 + -1x2 -1 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + x + x2)' equal to zero and attempt to solve: Simplifying 1 + x + x2 = 0 Solving 1 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x + x2 = 0 + -1 x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x + x2 = -1 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 = -1 + 0.25 Reorder the terms: 0.25 + x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 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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