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Simplifying 5a2 + 9a = 5 Reorder the terms: 9a + 5a2 = 5 Solving 9a + 5a2 = 5 Solving for variable 'a'. Reorder the terms: -5 + 9a + 5a2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 9a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + 1.8a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.8a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 1.8a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.8a + a2 = 0 + 1 1.8a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.8a + a2 = 1 The a term is 1.8a. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8a + 0.81 + a2 = 1 + 0.81 Reorder the terms: 0.81 + 1.8a + a2 = 1 + 0.81 Combine like terms: 1 + 0.81 = 1.81 0.81 + 1.8a + a2 = 1.81 Factor a perfect square on the left side: (a + 0.9)(a + 0.9) = 1.81 Calculate the square root of the right side: 1.345362405 Break this problem into two subproblems by setting (a + 0.9) equal to 1.345362405 and -1.345362405.Subproblem 1
a + 0.9 = 1.345362405 Simplifying a + 0.9 = 1.345362405 Reorder the terms: 0.9 + a = 1.345362405 Solving 0.9 + a = 1.345362405 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + a = 1.345362405 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + a = 1.345362405 + -0.9 a = 1.345362405 + -0.9 Combine like terms: 1.345362405 + -0.9 = 0.445362405 a = 0.445362405 Simplifying a = 0.445362405Subproblem 2
a + 0.9 = -1.345362405 Simplifying a + 0.9 = -1.345362405 Reorder the terms: 0.9 + a = -1.345362405 Solving 0.9 + a = -1.345362405 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + a = -1.345362405 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + a = -1.345362405 + -0.9 a = -1.345362405 + -0.9 Combine like terms: -1.345362405 + -0.9 = -2.245362405 a = -2.245362405 Simplifying a = -2.245362405Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.445362405, -2.245362405}
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