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Simplifying 8a2 + -16a + 5 = 0 Reorder the terms: 5 + -16a + 8a2 = 0 Solving 5 + -16a + 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'. 0.625 + -2a + a2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -2a + -0.625 + a2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -2a + a2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -2a + a2 = 0 + -0.625 -2a + a2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -2a + a2 = -0.625 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = -0.625 + 1 Reorder the terms: 1 + -2a + a2 = -0.625 + 1 Combine like terms: -0.625 + 1 = 0.375 1 + -2a + a2 = 0.375 Factor a perfect square on the left side: (a + -1)(a + -1) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (a + -1) equal to 0.612372436 and -0.612372436.Subproblem 1
a + -1 = 0.612372436 Simplifying a + -1 = 0.612372436 Reorder the terms: -1 + a = 0.612372436 Solving -1 + a = 0.612372436 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 0.612372436 + 1 Combine like terms: -1 + 1 = 0 0 + a = 0.612372436 + 1 a = 0.612372436 + 1 Combine like terms: 0.612372436 + 1 = 1.612372436 a = 1.612372436 Simplifying a = 1.612372436Subproblem 2
a + -1 = -0.612372436 Simplifying a + -1 = -0.612372436 Reorder the terms: -1 + a = -0.612372436 Solving -1 + a = -0.612372436 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -0.612372436 + 1 Combine like terms: -1 + 1 = 0 0 + a = -0.612372436 + 1 a = -0.612372436 + 1 Combine like terms: -0.612372436 + 1 = 0.387627564 a = 0.387627564 Simplifying a = 0.387627564Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.612372436, 0.387627564}
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