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Simplifying x = (x + 1)(x + 3) Reorder the terms: x = (1 + x)(x + 3) Reorder the terms: x = (1 + x)(3 + x) Multiply (1 + x) * (3 + x) x = (1(3 + x) + x(3 + x)) x = ((3 * 1 + x * 1) + x(3 + x)) x = ((3 + 1x) + x(3 + x)) x = (3 + 1x + (3 * x + x * x)) x = (3 + 1x + (3x + x2)) Combine like terms: 1x + 3x = 4x x = (3 + 4x + x2) Solving x = 3 + 4x + x2 Solving for variable 'x'. Reorder the terms: -3 + x + -4x + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Combine like terms: x + -4x = -3x -3 + -3x + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Reorder the terms: -3 + -3x + -1x2 = 3 + -3 + 4x + -4x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -3 + -3x + -1x2 = 0 + 4x + -4x + x2 + -1x2 -3 + -3x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -3 + -3x + -1x2 = 0 + x2 + -1x2 -3 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + -3x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 3x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 3x + x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + x2 = 0 Solving 3 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3x + x2 = 0 + -3 3x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3x + x2 = -3 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 = -3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -3 + 2.25 Combine like terms: -3 + 2.25 = -0.75 2.25 + 3x + x2 = -0.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -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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