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Simplifying 3(x + -4) = 6x2 + -12x Reorder the terms: 3(-4 + x) = 6x2 + -12x (-4 * 3 + x * 3) = 6x2 + -12x (-12 + 3x) = 6x2 + -12x Reorder the terms: -12 + 3x = -12x + 6x2 Solving -12 + 3x = -12x + 6x2 Solving for variable 'x'. Combine like terms: 3x + 12x = 15x -12 + 15x + -6x2 = -12x + 6x2 + 12x + -6x2 Reorder the terms: -12 + 15x + -6x2 = -12x + 12x + 6x2 + -6x2 Combine like terms: -12x + 12x = 0 -12 + 15x + -6x2 = 0 + 6x2 + -6x2 -12 + 15x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -12 + 15x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 5x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 5x + -2x2)' equal to zero and attempt to solve: Simplifying -4 + 5x + -2x2 = 0 Solving -4 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2 + -2.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.5x + x2 = 0 + -2 -2.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.5x + x2 = -2 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -2 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -2 + 1.5625 Combine like terms: -2 + 1.5625 = -0.4375 1.5625 + -2.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -0.4375 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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