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Simplifying 8(a2) + 3a + -399 = 0 Reorder the terms: -399 + 3a + 8a2 = 0 Solving -399 + 3a + 8a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -49.875 + 0.375a + a2 = 0 Move the constant term to the right: Add '49.875' to each side of the equation. -49.875 + 0.375a + 49.875 + a2 = 0 + 49.875 Reorder the terms: -49.875 + 49.875 + 0.375a + a2 = 0 + 49.875 Combine like terms: -49.875 + 49.875 = 0.000 0.000 + 0.375a + a2 = 0 + 49.875 0.375a + a2 = 0 + 49.875 Combine like terms: 0 + 49.875 = 49.875 0.375a + a2 = 49.875 The a term is 0.375a. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375a + 0.03515625 + a2 = 49.875 + 0.03515625 Reorder the terms: 0.03515625 + 0.375a + a2 = 49.875 + 0.03515625 Combine like terms: 49.875 + 0.03515625 = 49.91015625 0.03515625 + 0.375a + a2 = 49.91015625 Factor a perfect square on the left side: (a + 0.1875)(a + 0.1875) = 49.91015625 Calculate the square root of the right side: 7.064712043 Break this problem into two subproblems by setting (a + 0.1875) equal to 7.064712043 and -7.064712043.Subproblem 1
a + 0.1875 = 7.064712043 Simplifying a + 0.1875 = 7.064712043 Reorder the terms: 0.1875 + a = 7.064712043 Solving 0.1875 + a = 7.064712043 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + a = 7.064712043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + a = 7.064712043 + -0.1875 a = 7.064712043 + -0.1875 Combine like terms: 7.064712043 + -0.1875 = 6.877212043 a = 6.877212043 Simplifying a = 6.877212043Subproblem 2
a + 0.1875 = -7.064712043 Simplifying a + 0.1875 = -7.064712043 Reorder the terms: 0.1875 + a = -7.064712043 Solving 0.1875 + a = -7.064712043 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + a = -7.064712043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + a = -7.064712043 + -0.1875 a = -7.064712043 + -0.1875 Combine like terms: -7.064712043 + -0.1875 = -7.252212043 a = -7.252212043 Simplifying a = -7.252212043Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.877212043, -7.252212043}
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