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Simplifying 3a2 + -2a + -9 = 0 Reorder the terms: -9 + -2a + 3a2 = 0 Solving -9 + -2a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -0.6666666667a + a2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.6666666667a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + -0.6666666667a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.6666666667a + a2 = 0 + 3 -0.6666666667a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.6666666667a + a2 = 3 The a term is -0.6666666667a. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667a + 0.1111111112 + a2 = 3 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667a + a2 = 3 + 0.1111111112 Combine like terms: 3 + 0.1111111112 = 3.1111111112 0.1111111112 + -0.6666666667a + a2 = 3.1111111112 Factor a perfect square on the left side: (a + -0.3333333334)(a + -0.3333333334) = 3.1111111112 Calculate the square root of the right side: 1.763834207 Break this problem into two subproblems by setting (a + -0.3333333334) equal to 1.763834207 and -1.763834207.Subproblem 1
a + -0.3333333334 = 1.763834207 Simplifying a + -0.3333333334 = 1.763834207 Reorder the terms: -0.3333333334 + a = 1.763834207 Solving -0.3333333334 + a = 1.763834207 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + a = 1.763834207 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + a = 1.763834207 + 0.3333333334 a = 1.763834207 + 0.3333333334 Combine like terms: 1.763834207 + 0.3333333334 = 2.0971675404 a = 2.0971675404 Simplifying a = 2.0971675404Subproblem 2
a + -0.3333333334 = -1.763834207 Simplifying a + -0.3333333334 = -1.763834207 Reorder the terms: -0.3333333334 + a = -1.763834207 Solving -0.3333333334 + a = -1.763834207 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + a = -1.763834207 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + a = -1.763834207 + 0.3333333334 a = -1.763834207 + 0.3333333334 Combine like terms: -1.763834207 + 0.3333333334 = -1.4305008736 a = -1.4305008736 Simplifying a = -1.4305008736Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.0971675404, -1.4305008736}
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