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Simplifying 2x(4x + -4) + -3x = 9x + -24 Reorder the terms: 2x(-4 + 4x) + -3x = 9x + -24 (-4 * 2x + 4x * 2x) + -3x = 9x + -24 (-8x + 8x2) + -3x = 9x + -24 Reorder the terms: -8x + -3x + 8x2 = 9x + -24 Combine like terms: -8x + -3x = -11x -11x + 8x2 = 9x + -24 Reorder the terms: -11x + 8x2 = -24 + 9x Solving -11x + 8x2 = -24 + 9x Solving for variable 'x'. Reorder the terms: 24 + -11x + -9x + 8x2 = -24 + 9x + 24 + -9x Combine like terms: -11x + -9x = -20x 24 + -20x + 8x2 = -24 + 9x + 24 + -9x Reorder the terms: 24 + -20x + 8x2 = -24 + 24 + 9x + -9x Combine like terms: -24 + 24 = 0 24 + -20x + 8x2 = 0 + 9x + -9x 24 + -20x + 8x2 = 9x + -9x Combine like terms: 9x + -9x = 0 24 + -20x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -5x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + -5x + 2x2 = 0 Solving 6 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -2.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -2.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2.5x + x2 = 0 + -3 -2.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2.5x + x2 = -3 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 = -3 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -3 + 1.5625 Combine like terms: -3 + 1.5625 = -1.4375 1.5625 + -2.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -1.4375 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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