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Simplifying (x + 1) = (x + 2)(x + 2) + (x + 3) + (x + 3) Reorder the terms: (1 + x) = (x + 2)(x + 2) + (x + 3) + (x + 3) Remove parenthesis around (1 + x) 1 + x = (x + 2)(x + 2) + (x + 3) + (x + 3) Reorder the terms: 1 + x = (2 + x)(x + 2) + (x + 3) + (x + 3) Reorder the terms: 1 + x = (2 + x)(2 + x) + (x + 3) + (x + 3) Multiply (2 + x) * (2 + x) 1 + x = (2(2 + x) + x(2 + x)) + (x + 3) + (x + 3) 1 + x = ((2 * 2 + x * 2) + x(2 + x)) + (x + 3) + (x + 3) 1 + x = ((4 + 2x) + x(2 + x)) + (x + 3) + (x + 3) 1 + x = (4 + 2x + (2 * x + x * x)) + (x + 3) + (x + 3) 1 + x = (4 + 2x + (2x + x2)) + (x + 3) + (x + 3) Combine like terms: 2x + 2x = 4x 1 + x = (4 + 4x + x2) + (x + 3) + (x + 3) Reorder the terms: 1 + x = 4 + 4x + x2 + (3 + x) + (x + 3) Remove parenthesis around (3 + x) 1 + x = 4 + 4x + x2 + 3 + x + (x + 3) Reorder the terms: 1 + x = 4 + 4x + x2 + 3 + x + (3 + x) Remove parenthesis around (3 + x) 1 + x = 4 + 4x + x2 + 3 + x + 3 + x Reorder the terms: 1 + x = 4 + 3 + 3 + 4x + x + x + x2 Combine like terms: 4 + 3 = 7 1 + x = 7 + 3 + 4x + x + x + x2 Combine like terms: 7 + 3 = 10 1 + x = 10 + 4x + x + x + x2 Combine like terms: 4x + x = 5x 1 + x = 10 + 5x + x + x2 Combine like terms: 5x + x = 6x 1 + x = 10 + 6x + x2 Solving 1 + x = 10 + 6x + x2 Solving for variable 'x'. Reorder the terms: 1 + -10 + x + -6x + -1x2 = 10 + 6x + x2 + -10 + -6x + -1x2 Combine like terms: 1 + -10 = -9 -9 + x + -6x + -1x2 = 10 + 6x + x2 + -10 + -6x + -1x2 Combine like terms: x + -6x = -5x -9 + -5x + -1x2 = 10 + 6x + x2 + -10 + -6x + -1x2 Reorder the terms: -9 + -5x + -1x2 = 10 + -10 + 6x + -6x + x2 + -1x2 Combine like terms: 10 + -10 = 0 -9 + -5x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -9 + -5x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -9 + -5x + -1x2 = 0 + x2 + -1x2 -9 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + -5x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 5x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 5x + x2)' equal to zero and attempt to solve: Simplifying 9 + 5x + x2 = 0 Solving 9 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5x + x2 = 0 + -9 5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 5x + x2 = -9 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -9 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -9 + 6.25 Combine like terms: -9 + 6.25 = -2.75 6.25 + 5x + x2 = -2.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -2.75 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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