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Simplifying a2 + 3a + 5 = 6 Reorder the terms: 5 + 3a + a2 = 6 Solving 5 + 3a + a2 = 6 Solving for variable 'a'. Reorder the terms: 5 + -6 + 3a + a2 = 6 + -6 Combine like terms: 5 + -6 = -1 -1 + 3a + a2 = 6 + -6 Combine like terms: 6 + -6 = 0 -1 + 3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 3a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 3a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3a + a2 = 0 + 1 3a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 3a + a2 = 1 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = 1 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + 3a + a2 = 3.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (a + 1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
a + 1.5 = 1.802775638 Simplifying a + 1.5 = 1.802775638 Reorder the terms: 1.5 + a = 1.802775638 Solving 1.5 + a = 1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 1.802775638 + -1.5 a = 1.802775638 + -1.5 Combine like terms: 1.802775638 + -1.5 = 0.302775638 a = 0.302775638 Simplifying a = 0.302775638Subproblem 2
a + 1.5 = -1.802775638 Simplifying a + 1.5 = -1.802775638 Reorder the terms: 1.5 + a = -1.802775638 Solving 1.5 + a = -1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -1.802775638 + -1.5 a = -1.802775638 + -1.5 Combine like terms: -1.802775638 + -1.5 = -3.302775638 a = -3.302775638 Simplifying a = -3.302775638Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.302775638, -3.302775638}
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