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Simplifying 7a + -21 = 6a(a + -2) Reorder the terms: -21 + 7a = 6a(a + -2) Reorder the terms: -21 + 7a = 6a(-2 + a) -21 + 7a = (-2 * 6a + a * 6a) -21 + 7a = (-12a + 6a2) Solving -21 + 7a = -12a + 6a2 Solving for variable 'a'. Combine like terms: 7a + 12a = 19a -21 + 19a + -6a2 = -12a + 6a2 + 12a + -6a2 Reorder the terms: -21 + 19a + -6a2 = -12a + 12a + 6a2 + -6a2 Combine like terms: -12a + 12a = 0 -21 + 19a + -6a2 = 0 + 6a2 + -6a2 -21 + 19a + -6a2 = 6a2 + -6a2 Combine like terms: 6a2 + -6a2 = 0 -21 + 19a + -6a2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 3.5 + -3.166666667a + a2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -3.166666667a + -3.5 + a2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -3.166666667a + a2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -3.166666667a + a2 = 0 + -3.5 -3.166666667a + a2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -3.166666667a + a2 = -3.5 The a term is -3.166666667a. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667a + 2.506944447 + a2 = -3.5 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667a + a2 = -3.5 + 2.506944447 Combine like terms: -3.5 + 2.506944447 = -0.993055553 2.506944447 + -3.166666667a + a2 = -0.993055553 Factor a perfect square on the left side: (a + -1.583333334)(a + -1.583333334) = -0.993055553 Can't calculate square root of the right side. The solution to this equation could not be determined.
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