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Simplifying 5x(2x + -1) + -1(-3x) + -4x2 = -2 Reorder the terms: 5x(-1 + 2x) + -1(-3x) + -4x2 = -2 (-1 * 5x + 2x * 5x) + -1(-3x) + -4x2 = -2 (-5x + 10x2) + -1(-3x) + -4x2 = -2 Remove parenthesis around (-3x) -5x + 10x2 + -1 * -3x + -4x2 = -2 Multiply -1 * -3 -5x + 10x2 + 3x + -4x2 = -2 Reorder the terms: -5x + 3x + 10x2 + -4x2 = -2 Combine like terms: -5x + 3x = -2x -2x + 10x2 + -4x2 = -2 Combine like terms: 10x2 + -4x2 = 6x2 -2x + 6x2 = -2 Solving -2x + 6x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -2x + 6x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -1x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + -1x + 3x2 = 0 Solving 1 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.3333333333x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.3333333333x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + -0.3333333333 -0.3333333333x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.3333333333x + x2 = -0.3333333333 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = -0.3333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = -0.3333333333 + 0.02777777779 Combine like terms: -0.3333333333 + 0.02777777779 = -0.30555555551 0.02777777779 + -0.3333333333x + x2 = -0.30555555551 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = -0.30555555551 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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