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Simplifying (a + -4)(a + -4) = 12 Reorder the terms: (-4 + a)(a + -4) = 12 Reorder the terms: (-4 + a)(-4 + a) = 12 Multiply (-4 + a) * (-4 + a) (-4(-4 + a) + a(-4 + a)) = 12 ((-4 * -4 + a * -4) + a(-4 + a)) = 12 ((16 + -4a) + a(-4 + a)) = 12 (16 + -4a + (-4 * a + a * a)) = 12 (16 + -4a + (-4a + a2)) = 12 Combine like terms: -4a + -4a = -8a (16 + -8a + a2) = 12 Solving 16 + -8a + a2 = 12 Solving for variable 'a'. Reorder the terms: 16 + -12 + -8a + a2 = 12 + -12 Combine like terms: 16 + -12 = 4 4 + -8a + a2 = 12 + -12 Combine like terms: 12 + -12 = 0 4 + -8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -8a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8a + a2 = 0 + -4 -8a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -8a + a2 = -4 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = -4 + 16 Reorder the terms: 16 + -8a + a2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8a + a2 = 12 Factor a perfect square on the left side: (a + -4)(a + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (a + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
a + -4 = 3.464101615 Simplifying a + -4 = 3.464101615 Reorder the terms: -4 + a = 3.464101615 Solving -4 + a = 3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + a = 3.464101615 + 4 a = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 a = 7.464101615 Simplifying a = 7.464101615Subproblem 2
a + -4 = -3.464101615 Simplifying a + -4 = -3.464101615 Reorder the terms: -4 + a = -3.464101615 Solving -4 + a = -3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + a = -3.464101615 + 4 a = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 a = 0.535898385 Simplifying a = 0.535898385Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.464101615, 0.535898385}
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