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Simplifying a2 + 7a + 7a = 2 Reorder the terms: 7a + 7a + a2 = 2 Combine like terms: 7a + 7a = 14a 14a + a2 = 2 Solving 14a + a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + 14a + a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 14a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 14a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 14a + a2 = 0 + 2 14a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 14a + a2 = 2 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 = 2 + 49 Reorder the terms: 49 + 14a + a2 = 2 + 49 Combine like terms: 2 + 49 = 51 49 + 14a + a2 = 51 Factor a perfect square on the left side: (a + 7)(a + 7) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (a + 7) equal to 7.141428429 and -7.141428429.Subproblem 1
a + 7 = 7.141428429 Simplifying a + 7 = 7.141428429 Reorder the terms: 7 + a = 7.141428429 Solving 7 + a = 7.141428429 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 = 7.141428429 + -7 Combine like terms: 7 + -7 = 0 0 + a = 7.141428429 + -7 a = 7.141428429 + -7 Combine like terms: 7.141428429 + -7 = 0.141428429 a = 0.141428429 Simplifying a = 0.141428429Subproblem 2
a + 7 = -7.141428429 Simplifying a + 7 = -7.141428429 Reorder the terms: 7 + a = -7.141428429 Solving 7 + a = -7.141428429 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 = -7.141428429 + -7 Combine like terms: 7 + -7 = 0 0 + a = -7.141428429 + -7 a = -7.141428429 + -7 Combine like terms: -7.141428429 + -7 = -14.141428429 a = -14.141428429 Simplifying a = -14.141428429Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.141428429, -14.141428429}
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