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Simplifying 4(3x + -2) + -2x(4x + -6) + -24 = 0 Reorder the terms: 4(-2 + 3x) + -2x(4x + -6) + -24 = 0 (-2 * 4 + 3x * 4) + -2x(4x + -6) + -24 = 0 (-8 + 12x) + -2x(4x + -6) + -24 = 0 Reorder the terms: -8 + 12x + -2x(-6 + 4x) + -24 = 0 -8 + 12x + (-6 * -2x + 4x * -2x) + -24 = 0 -8 + 12x + (12x + -8x2) + -24 = 0 Reorder the terms: -8 + -24 + 12x + 12x + -8x2 = 0 Combine like terms: -8 + -24 = -32 -32 + 12x + 12x + -8x2 = 0 Combine like terms: 12x + 12x = 24x -32 + 24x + -8x2 = 0 Solving -32 + 24x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-4 + 3x + -1x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-4 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + -1x2 = 0 Solving -4 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -3x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x + x2 = 0 + -4 -3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3x + x2 = -4 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 = -4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3x + x2 = -1.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -1.75 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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