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Simplifying 7x(-3x + -1) = 2 Reorder the terms: 7x(-1 + -3x) = 2 (-1 * 7x + -3x * 7x) = 2 (-7x + -21x2) = 2 Solving -7x + -21x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -7x + -21x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -7x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 7x + 21x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 7x + 21x2)' equal to zero and attempt to solve: Simplifying 2 + 7x + 21x2 = 0 Solving 2 + 7x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.09523809524 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.09523809524' to each side of the equation. 0.09523809524 + 0.3333333333x + -0.09523809524 + x2 = 0 + -0.09523809524 Reorder the terms: 0.09523809524 + -0.09523809524 + 0.3333333333x + x2 = 0 + -0.09523809524 Combine like terms: 0.09523809524 + -0.09523809524 = 0.00000000000 0.00000000000 + 0.3333333333x + x2 = 0 + -0.09523809524 0.3333333333x + x2 = 0 + -0.09523809524 Combine like terms: 0 + -0.09523809524 = -0.09523809524 0.3333333333x + x2 = -0.09523809524 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 = -0.09523809524 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.09523809524 + 0.02777777779 Combine like terms: -0.09523809524 + 0.02777777779 = -0.06746031745 0.02777777779 + 0.3333333333x + x2 = -0.06746031745 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.06746031745 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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