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Simplifying a2 + 2a = 238 Reorder the terms: 2a + a2 = 238 Solving 2a + a2 = 238 Solving for variable 'a'. Reorder the terms: -238 + 2a + a2 = 238 + -238 Combine like terms: 238 + -238 = 0 -238 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '238' to each side of the equation. -238 + 2a + 238 + a2 = 0 + 238 Reorder the terms: -238 + 238 + 2a + a2 = 0 + 238 Combine like terms: -238 + 238 = 0 0 + 2a + a2 = 0 + 238 2a + a2 = 0 + 238 Combine like terms: 0 + 238 = 238 2a + a2 = 238 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 238 + 1 Reorder the terms: 1 + 2a + a2 = 238 + 1 Combine like terms: 238 + 1 = 239 1 + 2a + a2 = 239 Factor a perfect square on the left side: (a + 1)(a + 1) = 239 Calculate the square root of the right side: 15.459624834 Break this problem into two subproblems by setting (a + 1) equal to 15.459624834 and -15.459624834.Subproblem 1
a + 1 = 15.459624834 Simplifying a + 1 = 15.459624834 Reorder the terms: 1 + a = 15.459624834 Solving 1 + a = 15.459624834 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 15.459624834 + -1 Combine like terms: 1 + -1 = 0 0 + a = 15.459624834 + -1 a = 15.459624834 + -1 Combine like terms: 15.459624834 + -1 = 14.459624834 a = 14.459624834 Simplifying a = 14.459624834Subproblem 2
a + 1 = -15.459624834 Simplifying a + 1 = -15.459624834 Reorder the terms: 1 + a = -15.459624834 Solving 1 + a = -15.459624834 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -15.459624834 + -1 Combine like terms: 1 + -1 = 0 0 + a = -15.459624834 + -1 a = -15.459624834 + -1 Combine like terms: -15.459624834 + -1 = -16.459624834 a = -16.459624834 Simplifying a = -16.459624834Solution
The solution to the problem is based on the solutions from the subproblems. a = {14.459624834, -16.459624834}
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