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Simplifying 5a + -3 = a2 Reorder the terms: -3 + 5a = a2 Solving -3 + 5a = a2 Solving for variable 'a'. Combine like terms: a2 + -1a2 = 0 -3 + 5a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -5a + a2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5a + -3 + a2 = 0 + -3 Reorder the terms: 3 + -3 + -5a + a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5a + a2 = 0 + -3 -5a + a2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5a + a2 = -3 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = -3 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5a + a2 = 3.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (a + -2.5) equal to 1.802775638 and -1.802775638.Subproblem 1
a + -2.5 = 1.802775638 Simplifying a + -2.5 = 1.802775638 Reorder the terms: -2.5 + a = 1.802775638 Solving -2.5 + a = 1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 1.802775638 + 2.5 a = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 a = 4.302775638 Simplifying a = 4.302775638Subproblem 2
a + -2.5 = -1.802775638 Simplifying a + -2.5 = -1.802775638 Reorder the terms: -2.5 + a = -1.802775638 Solving -2.5 + a = -1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -1.802775638 + 2.5 a = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 a = 0.697224362 Simplifying a = 0.697224362Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.302775638, 0.697224362}
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