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Simplifying (a + 7)(a + -1) = -4 Reorder the terms: (7 + a)(a + -1) = -4 Reorder the terms: (7 + a)(-1 + a) = -4 Multiply (7 + a) * (-1 + a) (7(-1 + a) + a(-1 + a)) = -4 ((-1 * 7 + a * 7) + a(-1 + a)) = -4 ((-7 + 7a) + a(-1 + a)) = -4 (-7 + 7a + (-1 * a + a * a)) = -4 (-7 + 7a + (-1a + a2)) = -4 Combine like terms: 7a + -1a = 6a (-7 + 6a + a2) = -4 Solving -7 + 6a + a2 = -4 Solving for variable 'a'. Reorder the terms: -7 + 4 + 6a + a2 = -4 + 4 Combine like terms: -7 + 4 = -3 -3 + 6a + a2 = -4 + 4 Combine like terms: -4 + 4 = 0 -3 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 6a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + 6a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6a + a2 = 0 + 3 6a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 6a + a2 = 3 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 3 + 9 Reorder the terms: 9 + 6a + a2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6a + a2 = 12 Factor a perfect square on the left side: (a + 3)(a + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (a + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
a + 3 = 3.464101615 Simplifying a + 3 = 3.464101615 Reorder the terms: 3 + a = 3.464101615 Solving 3 + a = 3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.464101615 + -3 a = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 a = 0.464101615 Simplifying a = 0.464101615Subproblem 2
a + 3 = -3.464101615 Simplifying a + 3 = -3.464101615 Reorder the terms: 3 + a = -3.464101615 Solving 3 + a = -3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.464101615 + -3 a = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 a = -6.464101615 Simplifying a = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.464101615, -6.464101615}
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