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Simplifying -1(x + 6)(2x + 3) = x + -6x + -2x Reorder the terms: -1(6 + x)(2x + 3) = x + -6x + -2x Reorder the terms: -1(6 + x)(3 + 2x) = x + -6x + -2x Multiply (6 + x) * (3 + 2x) -1(6(3 + 2x) + x(3 + 2x)) = x + -6x + -2x -1((3 * 6 + 2x * 6) + x(3 + 2x)) = x + -6x + -2x -1((18 + 12x) + x(3 + 2x)) = x + -6x + -2x -1(18 + 12x + (3 * x + 2x * x)) = x + -6x + -2x -1(18 + 12x + (3x + 2x2)) = x + -6x + -2x Combine like terms: 12x + 3x = 15x -1(18 + 15x + 2x2) = x + -6x + -2x (18 * -1 + 15x * -1 + 2x2 * -1) = x + -6x + -2x (-18 + -15x + -2x2) = x + -6x + -2x Combine like terms: x + -6x = -5x -18 + -15x + -2x2 = -5x + -2x Combine like terms: -5x + -2x = -7x -18 + -15x + -2x2 = -7x Solving -18 + -15x + -2x2 = -7x Solving for variable 'x'. Reorder the terms: -18 + -15x + 7x + -2x2 = -7x + 7x Combine like terms: -15x + 7x = -8x -18 + -8x + -2x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -18 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 4x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(9 + 4x + x2)' equal to zero and attempt to solve: Simplifying 9 + 4x + x2 = 0 Solving 9 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 4x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 4x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x + x2 = 0 + -9 4x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 4x + x2 = -9 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -9 + 4 Reorder the terms: 4 + 4x + x2 = -9 + 4 Combine like terms: -9 + 4 = -5 4 + 4x + x2 = -5 Factor a perfect square on the left side: (x + 2)(x + 2) = -5 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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