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Simplifying a2 + 14a = 45 Reorder the terms: 14a + a2 = 45 Solving 14a + a2 = 45 Solving for variable 'a'. Reorder the terms: -45 + 14a + a2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 14a + 45 + a2 = 0 + 45 Reorder the terms: -45 + 45 + 14a + a2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 14a + a2 = 0 + 45 14a + a2 = 0 + 45 Combine like terms: 0 + 45 = 45 14a + a2 = 45 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 = 45 + 49 Reorder the terms: 49 + 14a + a2 = 45 + 49 Combine like terms: 45 + 49 = 94 49 + 14a + a2 = 94 Factor a perfect square on the left side: (a + 7)(a + 7) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (a + 7) equal to 9.695359715 and -9.695359715.Subproblem 1
a + 7 = 9.695359715 Simplifying a + 7 = 9.695359715 Reorder the terms: 7 + a = 9.695359715 Solving 7 + a = 9.695359715 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 = 9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + a = 9.695359715 + -7 a = 9.695359715 + -7 Combine like terms: 9.695359715 + -7 = 2.695359715 a = 2.695359715 Simplifying a = 2.695359715Subproblem 2
a + 7 = -9.695359715 Simplifying a + 7 = -9.695359715 Reorder the terms: 7 + a = -9.695359715 Solving 7 + a = -9.695359715 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 = -9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + a = -9.695359715 + -7 a = -9.695359715 + -7 Combine like terms: -9.695359715 + -7 = -16.695359715 a = -16.695359715 Simplifying a = -16.695359715Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.695359715, -16.695359715}
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