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Simplifying -5x(4x + -4) + -2x = 3x + 45 Reorder the terms: -5x(-4 + 4x) + -2x = 3x + 45 (-4 * -5x + 4x * -5x) + -2x = 3x + 45 (20x + -20x2) + -2x = 3x + 45 Reorder the terms: 20x + -2x + -20x2 = 3x + 45 Combine like terms: 20x + -2x = 18x 18x + -20x2 = 3x + 45 Reorder the terms: 18x + -20x2 = 45 + 3x Solving 18x + -20x2 = 45 + 3x Solving for variable 'x'. Reorder the terms: -45 + 18x + -3x + -20x2 = 45 + 3x + -45 + -3x Combine like terms: 18x + -3x = 15x -45 + 15x + -20x2 = 45 + 3x + -45 + -3x Reorder the terms: -45 + 15x + -20x2 = 45 + -45 + 3x + -3x Combine like terms: 45 + -45 = 0 -45 + 15x + -20x2 = 0 + 3x + -3x -45 + 15x + -20x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -45 + 15x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 3x + -4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying -9 + 3x + -4x2 = 0 Solving -9 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -0.75x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -0.75x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -0.75x + x2 = 0 + -2.25 -0.75x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -0.75x + x2 = -2.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -2.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -2.25 + 0.140625 Combine like terms: -2.25 + 0.140625 = -2.109375 0.140625 + -0.75x + x2 = -2.109375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -2.109375 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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