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Simplifying x(x + 4) = (x + 2)(2x + 3) Reorder the terms: x(4 + x) = (x + 2)(2x + 3) (4 * x + x * x) = (x + 2)(2x + 3) (4x + x2) = (x + 2)(2x + 3) Reorder the terms: 4x + x2 = (2 + x)(2x + 3) Reorder the terms: 4x + x2 = (2 + x)(3 + 2x) Multiply (2 + x) * (3 + 2x) 4x + x2 = (2(3 + 2x) + x(3 + 2x)) 4x + x2 = ((3 * 2 + 2x * 2) + x(3 + 2x)) 4x + x2 = ((6 + 4x) + x(3 + 2x)) 4x + x2 = (6 + 4x + (3 * x + 2x * x)) 4x + x2 = (6 + 4x + (3x + 2x2)) Combine like terms: 4x + 3x = 7x 4x + x2 = (6 + 7x + 2x2) Solving 4x + x2 = 6 + 7x + 2x2 Solving for variable 'x'. Reorder the terms: -6 + 4x + -7x + x2 + -2x2 = 6 + 7x + 2x2 + -6 + -7x + -2x2 Combine like terms: 4x + -7x = -3x -6 + -3x + x2 + -2x2 = 6 + 7x + 2x2 + -6 + -7x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -6 + -3x + -1x2 = 6 + 7x + 2x2 + -6 + -7x + -2x2 Reorder the terms: -6 + -3x + -1x2 = 6 + -6 + 7x + -7x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 -6 + -3x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2 -6 + -3x + -1x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 -6 + -3x + -1x2 = 0 + 2x2 + -2x2 -6 + -3x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -3x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 3x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 3x + x2)' equal to zero and attempt to solve: Simplifying 6 + 3x + x2 = 0 Solving 6 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 3x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 3x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 3x + x2 = 0 + -6 3x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 3x + x2 = -6 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 = -6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -6 + 2.25 Combine like terms: -6 + 2.25 = -3.75 2.25 + 3x + x2 = -3.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -3.75 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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