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Simplifying 15a2 + -16a + -3 = 0 Reorder the terms: -3 + -16a + 15a2 = 0 Solving -3 + -16a + 15a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2 + -1.066666667a + a2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.066666667a + 0.2 + a2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.066666667a + a2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.066666667a + a2 = 0 + 0.2 -1.066666667a + a2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.066666667a + a2 = 0.2 The a term is -1.066666667a. Take half its coefficient (-0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. -1.066666667a + 0.2844444446 + a2 = 0.2 + 0.2844444446 Reorder the terms: 0.2844444446 + -1.066666667a + a2 = 0.2 + 0.2844444446 Combine like terms: 0.2 + 0.2844444446 = 0.4844444446 0.2844444446 + -1.066666667a + a2 = 0.4844444446 Factor a perfect square on the left side: (a + -0.5333333335)(a + -0.5333333335) = 0.4844444446 Calculate the square root of the right side: 0.696020434 Break this problem into two subproblems by setting (a + -0.5333333335) equal to 0.696020434 and -0.696020434.Subproblem 1
a + -0.5333333335 = 0.696020434 Simplifying a + -0.5333333335 = 0.696020434 Reorder the terms: -0.5333333335 + a = 0.696020434 Solving -0.5333333335 + a = 0.696020434 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + a = 0.696020434 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + a = 0.696020434 + 0.5333333335 a = 0.696020434 + 0.5333333335 Combine like terms: 0.696020434 + 0.5333333335 = 1.2293537675 a = 1.2293537675 Simplifying a = 1.2293537675Subproblem 2
a + -0.5333333335 = -0.696020434 Simplifying a + -0.5333333335 = -0.696020434 Reorder the terms: -0.5333333335 + a = -0.696020434 Solving -0.5333333335 + a = -0.696020434 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + a = -0.696020434 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + a = -0.696020434 + 0.5333333335 a = -0.696020434 + 0.5333333335 Combine like terms: -0.696020434 + 0.5333333335 = -0.1626871005 a = -0.1626871005 Simplifying a = -0.1626871005Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.2293537675, -0.1626871005}
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