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Simplifying a * a + 42a + -12 = 0 Multiply a * a a2 + 42a + -12 = 0 Reorder the terms: -12 + 42a + a2 = 0 Solving -12 + 42a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 42a + 12 + a2 = 0 + 12 Reorder the terms: -12 + 12 + 42a + a2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 42a + a2 = 0 + 12 42a + a2 = 0 + 12 Combine like terms: 0 + 12 = 12 42a + a2 = 12 The a term is 42a. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42a + 441 + a2 = 12 + 441 Reorder the terms: 441 + 42a + a2 = 12 + 441 Combine like terms: 12 + 441 = 453 441 + 42a + a2 = 453 Factor a perfect square on the left side: (a + 21)(a + 21) = 453 Calculate the square root of the right side: 21.283796654 Break this problem into two subproblems by setting (a + 21) equal to 21.283796654 and -21.283796654.Subproblem 1
a + 21 = 21.283796654 Simplifying a + 21 = 21.283796654 Reorder the terms: 21 + a = 21.283796654 Solving 21 + a = 21.283796654 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + a = 21.283796654 + -21 Combine like terms: 21 + -21 = 0 0 + a = 21.283796654 + -21 a = 21.283796654 + -21 Combine like terms: 21.283796654 + -21 = 0.283796654 a = 0.283796654 Simplifying a = 0.283796654Subproblem 2
a + 21 = -21.283796654 Simplifying a + 21 = -21.283796654 Reorder the terms: 21 + a = -21.283796654 Solving 21 + a = -21.283796654 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + a = -21.283796654 + -21 Combine like terms: 21 + -21 = 0 0 + a = -21.283796654 + -21 a = -21.283796654 + -21 Combine like terms: -21.283796654 + -21 = -42.283796654 a = -42.283796654 Simplifying a = -42.283796654Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.283796654, -42.283796654}
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