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Simplifying a + 36 + -1a2 = 0 Reorder the terms: 36 + a + -1a2 = 0 Solving 36 + a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -1a + a2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -1a + 36 + a2 = 0 + 36 Reorder the terms: -36 + 36 + -1a + a2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1a + a2 = 0 + 36 -1a + a2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1a + a2 = 36 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 36 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + -1a + a2 = 36.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (a + 0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
a + 0.5 = 6.020797289 Simplifying a + 0.5 = 6.020797289 Reorder the terms: 0.5 + a = 6.020797289 Solving 0.5 + a = 6.020797289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 6.020797289 + -0.5 a = 6.020797289 + -0.5 Combine like terms: 6.020797289 + -0.5 = 5.520797289 a = 5.520797289 Simplifying a = 5.520797289Subproblem 2
a + 0.5 = -6.020797289 Simplifying a + 0.5 = -6.020797289 Reorder the terms: 0.5 + a = -6.020797289 Solving 0.5 + a = -6.020797289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -6.020797289 + -0.5 a = -6.020797289 + -0.5 Combine like terms: -6.020797289 + -0.5 = -6.520797289 a = -6.520797289 Simplifying a = -6.520797289Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.520797289, -6.520797289}
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