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Simplifying a2 + 14a + -38 = 0 Reorder the terms: -38 + 14a + a2 = 0 Solving -38 + 14a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 14a + 38 + a2 = 0 + 38 Reorder the terms: -38 + 38 + 14a + a2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 14a + a2 = 0 + 38 14a + a2 = 0 + 38 Combine like terms: 0 + 38 = 38 14a + a2 = 38 The a term is 14a. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14a + 49 + a2 = 38 + 49 Reorder the terms: 49 + 14a + a2 = 38 + 49 Combine like terms: 38 + 49 = 87 49 + 14a + a2 = 87 Factor a perfect square on the left side: (a + 7)(a + 7) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (a + 7) equal to 9.327379053 and -9.327379053.Subproblem 1
a + 7 = 9.327379053 Simplifying a + 7 = 9.327379053 Reorder the terms: 7 + a = 9.327379053 Solving 7 + a = 9.327379053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 9.327379053 + -7 Combine like terms: 7 + -7 = 0 0 + a = 9.327379053 + -7 a = 9.327379053 + -7 Combine like terms: 9.327379053 + -7 = 2.327379053 a = 2.327379053 Simplifying a = 2.327379053Subproblem 2
a + 7 = -9.327379053 Simplifying a + 7 = -9.327379053 Reorder the terms: 7 + a = -9.327379053 Solving 7 + a = -9.327379053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = -9.327379053 + -7 Combine like terms: 7 + -7 = 0 0 + a = -9.327379053 + -7 a = -9.327379053 + -7 Combine like terms: -9.327379053 + -7 = -16.327379053 a = -16.327379053 Simplifying a = -16.327379053Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.327379053, -16.327379053}
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