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Simplifying 3x2 + 8x + -9 = x2 + -4x + -39 Reorder the terms: -9 + 8x + 3x2 = x2 + -4x + -39 Reorder the terms: -9 + 8x + 3x2 = -39 + -4x + x2 Solving -9 + 8x + 3x2 = -39 + -4x + x2 Solving for variable 'x'. Reorder the terms: -9 + 39 + 8x + 4x + 3x2 + -1x2 = -39 + -4x + x2 + 39 + 4x + -1x2 Combine like terms: -9 + 39 = 30 30 + 8x + 4x + 3x2 + -1x2 = -39 + -4x + x2 + 39 + 4x + -1x2 Combine like terms: 8x + 4x = 12x 30 + 12x + 3x2 + -1x2 = -39 + -4x + x2 + 39 + 4x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 30 + 12x + 2x2 = -39 + -4x + x2 + 39 + 4x + -1x2 Reorder the terms: 30 + 12x + 2x2 = -39 + 39 + -4x + 4x + x2 + -1x2 Combine like terms: -39 + 39 = 0 30 + 12x + 2x2 = 0 + -4x + 4x + x2 + -1x2 30 + 12x + 2x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 30 + 12x + 2x2 = 0 + x2 + -1x2 30 + 12x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 30 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 6x + x2)' equal to zero and attempt to solve: Simplifying 15 + 6x + x2 = 0 Solving 15 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 6x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 6x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 6x + x2 = 0 + -15 6x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 6x + x2 = -15 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -15 + 9 Reorder the terms: 9 + 6x + x2 = -15 + 9 Combine like terms: -15 + 9 = -6 9 + 6x + x2 = -6 Factor a perfect square on the left side: (x + 3)(x + 3) = -6 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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