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Simplifying 3a2 + -18a + -21 = -4 Reorder the terms: -21 + -18a + 3a2 = -4 Solving -21 + -18a + 3a2 = -4 Solving for variable 'a'. Reorder the terms: -21 + 4 + -18a + 3a2 = -4 + 4 Combine like terms: -21 + 4 = -17 -17 + -18a + 3a2 = -4 + 4 Combine like terms: -4 + 4 = 0 -17 + -18a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.666666667 + -6a + a2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + -6a + 5.666666667 + a2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + -6a + a2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + -6a + a2 = 0 + 5.666666667 -6a + a2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 -6a + a2 = 5.666666667 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = 5.666666667 + 9 Reorder the terms: 9 + -6a + a2 = 5.666666667 + 9 Combine like terms: 5.666666667 + 9 = 14.666666667 9 + -6a + a2 = 14.666666667 Factor a perfect square on the left side: (a + -3)(a + -3) = 14.666666667 Calculate the square root of the right side: 3.829708431 Break this problem into two subproblems by setting (a + -3) equal to 3.829708431 and -3.829708431.Subproblem 1
a + -3 = 3.829708431 Simplifying a + -3 = 3.829708431 Reorder the terms: -3 + a = 3.829708431 Solving -3 + a = 3.829708431 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 3.829708431 + 3 Combine like terms: -3 + 3 = 0 0 + a = 3.829708431 + 3 a = 3.829708431 + 3 Combine like terms: 3.829708431 + 3 = 6.829708431 a = 6.829708431 Simplifying a = 6.829708431Subproblem 2
a + -3 = -3.829708431 Simplifying a + -3 = -3.829708431 Reorder the terms: -3 + a = -3.829708431 Solving -3 + a = -3.829708431 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -3.829708431 + 3 Combine like terms: -3 + 3 = 0 0 + a = -3.829708431 + 3 a = -3.829708431 + 3 Combine like terms: -3.829708431 + 3 = -0.829708431 a = -0.829708431 Simplifying a = -0.829708431Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.829708431, -0.829708431}
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