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Simplifying 3.5a2 + 3.5a + -5 = 0 Reorder the terms: -5 + 3.5a + 3.5a2 = 0 Solving -5 + 3.5a + 3.5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -1.428571429 + a + a2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + a + 1.428571429 + a2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + a + a2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + a + a2 = 0 + 1.428571429 a + a2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 a + a2 = 1.428571429 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 1.428571429 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 1.428571429 + 0.25 Combine like terms: 1.428571429 + 0.25 = 1.678571429 1.25 + a2 = 1.678571429 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 1.678571429 Calculate the square root of the right side: 1.295596939 Break this problem into two subproblems by setting (a + 0.5) equal to 1.295596939 and -1.295596939.Subproblem 1
a + 0.5 = 1.295596939 Simplifying a + 0.5 = 1.295596939 Reorder the terms: 0.5 + a = 1.295596939 Solving 0.5 + a = 1.295596939 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 1.295596939 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 1.295596939 + -0.5 a = 1.295596939 + -0.5 Combine like terms: 1.295596939 + -0.5 = 0.795596939 a = 0.795596939 Simplifying a = 0.795596939Subproblem 2
a + 0.5 = -1.295596939 Simplifying a + 0.5 = -1.295596939 Reorder the terms: 0.5 + a = -1.295596939 Solving 0.5 + a = -1.295596939 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -1.295596939 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -1.295596939 + -0.5 a = -1.295596939 + -0.5 Combine like terms: -1.295596939 + -0.5 = -1.795596939 a = -1.795596939 Simplifying a = -1.795596939Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.795596939, -1.795596939}
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