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Simplifying 4x = (x + 3)(x + 4) Reorder the terms: 4x = (3 + x)(x + 4) Reorder the terms: 4x = (3 + x)(4 + x) Multiply (3 + x) * (4 + x) 4x = (3(4 + x) + x(4 + x)) 4x = ((4 * 3 + x * 3) + x(4 + x)) 4x = ((12 + 3x) + x(4 + x)) 4x = (12 + 3x + (4 * x + x * x)) 4x = (12 + 3x + (4x + x2)) Combine like terms: 3x + 4x = 7x 4x = (12 + 7x + x2) Solving 4x = 12 + 7x + x2 Solving for variable 'x'. Reorder the terms: -12 + 4x + -7x + -1x2 = 12 + 7x + x2 + -12 + -7x + -1x2 Combine like terms: 4x + -7x = -3x -12 + -3x + -1x2 = 12 + 7x + x2 + -12 + -7x + -1x2 Reorder the terms: -12 + -3x + -1x2 = 12 + -12 + 7x + -7x + x2 + -1x2 Combine like terms: 12 + -12 = 0 -12 + -3x + -1x2 = 0 + 7x + -7x + x2 + -1x2 -12 + -3x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 -12 + -3x + -1x2 = 0 + x2 + -1x2 -12 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -3x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 3x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 3x + x2)' equal to zero and attempt to solve: Simplifying 12 + 3x + x2 = 0 Solving 12 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 3x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 3x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 3x + x2 = 0 + -12 3x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 3x + x2 = -12 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 = -12 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -12 + 2.25 Combine like terms: -12 + 2.25 = -9.75 2.25 + 3x + x2 = -9.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -9.75 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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