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Simplifying -6x(x + -3) + 2(x + -6) = 2(4x + 9) Reorder the terms: -6x(-3 + x) + 2(x + -6) = 2(4x + 9) (-3 * -6x + x * -6x) + 2(x + -6) = 2(4x + 9) (18x + -6x2) + 2(x + -6) = 2(4x + 9) Reorder the terms: 18x + -6x2 + 2(-6 + x) = 2(4x + 9) 18x + -6x2 + (-6 * 2 + x * 2) = 2(4x + 9) 18x + -6x2 + (-12 + 2x) = 2(4x + 9) Reorder the terms: -12 + 18x + 2x + -6x2 = 2(4x + 9) Combine like terms: 18x + 2x = 20x -12 + 20x + -6x2 = 2(4x + 9) Reorder the terms: -12 + 20x + -6x2 = 2(9 + 4x) -12 + 20x + -6x2 = (9 * 2 + 4x * 2) -12 + 20x + -6x2 = (18 + 8x) Solving -12 + 20x + -6x2 = 18 + 8x Solving for variable 'x'. Reorder the terms: -12 + -18 + 20x + -8x + -6x2 = 18 + 8x + -18 + -8x Combine like terms: -12 + -18 = -30 -30 + 20x + -8x + -6x2 = 18 + 8x + -18 + -8x Combine like terms: 20x + -8x = 12x -30 + 12x + -6x2 = 18 + 8x + -18 + -8x Reorder the terms: -30 + 12x + -6x2 = 18 + -18 + 8x + -8x Combine like terms: 18 + -18 = 0 -30 + 12x + -6x2 = 0 + 8x + -8x -30 + 12x + -6x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -30 + 12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + 2x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 2x + -1x2 = 0 Solving -5 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -2x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x + x2 = 0 + -5 -2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2x + x2 = -5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -5 + 1 Reorder the terms: 1 + -2x + x2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + -2x + x2 = -4 Factor a perfect square on the left side: (x + -1)(x + -1) = -4 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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