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Simplifying (5x + 6)(3x + -6) = -39 Reorder the terms: (6 + 5x)(3x + -6) = -39 Reorder the terms: (6 + 5x)(-6 + 3x) = -39 Multiply (6 + 5x) * (-6 + 3x) (6(-6 + 3x) + 5x * (-6 + 3x)) = -39 ((-6 * 6 + 3x * 6) + 5x * (-6 + 3x)) = -39 ((-36 + 18x) + 5x * (-6 + 3x)) = -39 (-36 + 18x + (-6 * 5x + 3x * 5x)) = -39 (-36 + 18x + (-30x + 15x2)) = -39 Combine like terms: 18x + -30x = -12x (-36 + -12x + 15x2) = -39 Solving -36 + -12x + 15x2 = -39 Solving for variable 'x'. Reorder the terms: -36 + 39 + -12x + 15x2 = -39 + 39 Combine like terms: -36 + 39 = 3 3 + -12x + 15x2 = -39 + 39 Combine like terms: -39 + 39 = 0 3 + -12x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -4x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + -4x + 5x2 = 0 Solving 1 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -0.8x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -0.8x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -0.8x + x2 = 0 + -0.2 -0.8x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -0.8x + x2 = -0.2 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.2 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.2 + 0.16 Combine like terms: -0.2 + 0.16 = -0.04 0.16 + -0.8x + x2 = -0.04 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = -0.04 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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