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Simplifying (2x + 3)(2x + 3) + 2x + -3(2x + -3) = (4x + 6) Reorder the terms: (3 + 2x)(2x + 3) + 2x + -3(2x + -3) = (4x + 6) Reorder the terms: (3 + 2x)(3 + 2x) + 2x + -3(2x + -3) = (4x + 6) Multiply (3 + 2x) * (3 + 2x) (3(3 + 2x) + 2x * (3 + 2x)) + 2x + -3(2x + -3) = (4x + 6) ((3 * 3 + 2x * 3) + 2x * (3 + 2x)) + 2x + -3(2x + -3) = (4x + 6) ((9 + 6x) + 2x * (3 + 2x)) + 2x + -3(2x + -3) = (4x + 6) (9 + 6x + (3 * 2x + 2x * 2x)) + 2x + -3(2x + -3) = (4x + 6) (9 + 6x + (6x + 4x2)) + 2x + -3(2x + -3) = (4x + 6) Combine like terms: 6x + 6x = 12x (9 + 12x + 4x2) + 2x + -3(2x + -3) = (4x + 6) Reorder the terms: 9 + 12x + 4x2 + 2x + -3(-3 + 2x) = (4x + 6) 9 + 12x + 4x2 + 2x + (-3 * -3 + 2x * -3) = (4x + 6) 9 + 12x + 4x2 + 2x + (9 + -6x) = (4x + 6) Reorder the terms: 9 + 9 + 12x + 2x + -6x + 4x2 = (4x + 6) Combine like terms: 9 + 9 = 18 18 + 12x + 2x + -6x + 4x2 = (4x + 6) Combine like terms: 12x + 2x = 14x 18 + 14x + -6x + 4x2 = (4x + 6) Combine like terms: 14x + -6x = 8x 18 + 8x + 4x2 = (4x + 6) Reorder the terms: 18 + 8x + 4x2 = (6 + 4x) Remove parenthesis around (6 + 4x) 18 + 8x + 4x2 = 6 + 4x Solving 18 + 8x + 4x2 = 6 + 4x Solving for variable 'x'. Reorder the terms: 18 + -6 + 8x + -4x + 4x2 = 6 + 4x + -6 + -4x Combine like terms: 18 + -6 = 12 12 + 8x + -4x + 4x2 = 6 + 4x + -6 + -4x Combine like terms: 8x + -4x = 4x 12 + 4x + 4x2 = 6 + 4x + -6 + -4x Reorder the terms: 12 + 4x + 4x2 = 6 + -6 + 4x + -4x Combine like terms: 6 + -6 = 0 12 + 4x + 4x2 = 0 + 4x + -4x 12 + 4x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 12 + 4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + x + x2)' equal to zero and attempt to solve: Simplifying 3 + x + x2 = 0 Solving 3 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x + x2 = 0 + -3 x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 x + x2 = -3 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 = -3 + 0.25 Reorder the terms: 0.25 + x + x2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + x + x2 = -2.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -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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