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Simplifying 0 = a2 + -6a + -100 Reorder the terms: 0 = -100 + -6a + a2 Solving 0 = -100 + -6a + a2 Solving for variable 'a'. Combine like terms: 0 + 100 = 100 100 + 6a + -1a2 = -100 + -6a + a2 + 100 + 6a + -1a2 Reorder the terms: 100 + 6a + -1a2 = -100 + 100 + -6a + 6a + a2 + -1a2 Combine like terms: -100 + 100 = 0 100 + 6a + -1a2 = 0 + -6a + 6a + a2 + -1a2 100 + 6a + -1a2 = -6a + 6a + a2 + -1a2 Combine like terms: -6a + 6a = 0 100 + 6a + -1a2 = 0 + a2 + -1a2 100 + 6a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 100 + 6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + -6a + a2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -6a + 100 + a2 = 0 + 100 Reorder the terms: -100 + 100 + -6a + a2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -6a + a2 = 0 + 100 -6a + a2 = 0 + 100 Combine like terms: 0 + 100 = 100 -6a + a2 = 100 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 = 100 + 9 Reorder the terms: 9 + -6a + a2 = 100 + 9 Combine like terms: 100 + 9 = 109 9 + -6a + a2 = 109 Factor a perfect square on the left side: (a + -3)(a + -3) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (a + -3) equal to 10.440306509 and -10.440306509.Subproblem 1
a + -3 = 10.440306509 Simplifying a + -3 = 10.440306509 Reorder the terms: -3 + a = 10.440306509 Solving -3 + a = 10.440306509 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 = 10.440306509 + 3 Combine like terms: -3 + 3 = 0 0 + a = 10.440306509 + 3 a = 10.440306509 + 3 Combine like terms: 10.440306509 + 3 = 13.440306509 a = 13.440306509 Simplifying a = 13.440306509Subproblem 2
a + -3 = -10.440306509 Simplifying a + -3 = -10.440306509 Reorder the terms: -3 + a = -10.440306509 Solving -3 + a = -10.440306509 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 = -10.440306509 + 3 Combine like terms: -3 + 3 = 0 0 + a = -10.440306509 + 3 a = -10.440306509 + 3 Combine like terms: -10.440306509 + 3 = -7.440306509 a = -7.440306509 Simplifying a = -7.440306509Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.440306509, -7.440306509}
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