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Simplifying -16a2 + 15a + -1 = 0 Reorder the terms: -1 + 15a + -16a2 = 0 Solving -1 + 15a + -16a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.0625 + -0.9375a + a2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -0.9375a + -0.0625 + a2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -0.9375a + a2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -0.9375a + a2 = 0 + -0.0625 -0.9375a + a2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -0.9375a + a2 = -0.0625 The a term is -0.9375a. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375a + 0.2197265625 + a2 = -0.0625 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375a + a2 = -0.0625 + 0.2197265625 Combine like terms: -0.0625 + 0.2197265625 = 0.1572265625 0.2197265625 + -0.9375a + a2 = 0.1572265625 Factor a perfect square on the left side: (a + -0.46875)(a + -0.46875) = 0.1572265625 Calculate the square root of the right side: 0.396518048 Break this problem into two subproblems by setting (a + -0.46875) equal to 0.396518048 and -0.396518048.Subproblem 1
a + -0.46875 = 0.396518048 Simplifying a + -0.46875 = 0.396518048 Reorder the terms: -0.46875 + a = 0.396518048 Solving -0.46875 + a = 0.396518048 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + a = 0.396518048 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + a = 0.396518048 + 0.46875 a = 0.396518048 + 0.46875 Combine like terms: 0.396518048 + 0.46875 = 0.865268048 a = 0.865268048 Simplifying a = 0.865268048Subproblem 2
a + -0.46875 = -0.396518048 Simplifying a + -0.46875 = -0.396518048 Reorder the terms: -0.46875 + a = -0.396518048 Solving -0.46875 + a = -0.396518048 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + a = -0.396518048 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + a = -0.396518048 + 0.46875 a = -0.396518048 + 0.46875 Combine like terms: -0.396518048 + 0.46875 = 0.072231952 a = 0.072231952 Simplifying a = 0.072231952Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.865268048, 0.072231952}
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