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Simplifying 5a2 + 2a = 27 Reorder the terms: 2a + 5a2 = 27 Solving 2a + 5a2 = 27 Solving for variable 'a'. Reorder the terms: -27 + 2a + 5a2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 2a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + 0.4a + a2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 0.4a + 5.4 + a2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 0.4a + a2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 0.4a + a2 = 0 + 5.4 0.4a + a2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 0.4a + a2 = 5.4 The a term is 0.4a. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4a + 0.04 + a2 = 5.4 + 0.04 Reorder the terms: 0.04 + 0.4a + a2 = 5.4 + 0.04 Combine like terms: 5.4 + 0.04 = 5.44 0.04 + 0.4a + a2 = 5.44 Factor a perfect square on the left side: (a + 0.2)(a + 0.2) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting (a + 0.2) equal to 2.332380758 and -2.332380758.Subproblem 1
a + 0.2 = 2.332380758 Simplifying a + 0.2 = 2.332380758 Reorder the terms: 0.2 + a = 2.332380758 Solving 0.2 + a = 2.332380758 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = 2.332380758 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = 2.332380758 + -0.2 a = 2.332380758 + -0.2 Combine like terms: 2.332380758 + -0.2 = 2.132380758 a = 2.132380758 Simplifying a = 2.132380758Subproblem 2
a + 0.2 = -2.332380758 Simplifying a + 0.2 = -2.332380758 Reorder the terms: 0.2 + a = -2.332380758 Solving 0.2 + a = -2.332380758 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = -2.332380758 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = -2.332380758 + -0.2 a = -2.332380758 + -0.2 Combine like terms: -2.332380758 + -0.2 = -2.532380758 a = -2.532380758 Simplifying a = -2.532380758Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.132380758, -2.532380758}
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