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Simplifying 141 = 3a + a2 Solving 141 = 3a + a2 Solving for variable 'a'. Reorder the terms: 141 + -3a + -1a2 = 3a + -3a + a2 + -1a2 Combine like terms: 3a + -3a = 0 141 + -3a + -1a2 = 0 + a2 + -1a2 141 + -3a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 141 + -3a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -141 + 3a + a2 = 0 Move the constant term to the right: Add '141' to each side of the equation. -141 + 3a + 141 + a2 = 0 + 141 Reorder the terms: -141 + 141 + 3a + a2 = 0 + 141 Combine like terms: -141 + 141 = 0 0 + 3a + a2 = 0 + 141 3a + a2 = 0 + 141 Combine like terms: 0 + 141 = 141 3a + a2 = 141 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 = 141 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 141 + 2.25 Combine like terms: 141 + 2.25 = 143.25 2.25 + 3a + a2 = 143.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 143.25 Calculate the square root of the right side: 11.968709204 Break this problem into two subproblems by setting (a + 1.5) equal to 11.968709204 and -11.968709204.Subproblem 1
a + 1.5 = 11.968709204 Simplifying a + 1.5 = 11.968709204 Reorder the terms: 1.5 + a = 11.968709204 Solving 1.5 + a = 11.968709204 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 = 11.968709204 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 11.968709204 + -1.5 a = 11.968709204 + -1.5 Combine like terms: 11.968709204 + -1.5 = 10.468709204 a = 10.468709204 Simplifying a = 10.468709204Subproblem 2
a + 1.5 = -11.968709204 Simplifying a + 1.5 = -11.968709204 Reorder the terms: 1.5 + a = -11.968709204 Solving 1.5 + a = -11.968709204 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 = -11.968709204 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -11.968709204 + -1.5 a = -11.968709204 + -1.5 Combine like terms: -11.968709204 + -1.5 = -13.468709204 a = -13.468709204 Simplifying a = -13.468709204Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.468709204, -13.468709204}
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