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Simplifying a2 + a + -22 = 0 Reorder the terms: -22 + a + a2 = 0 Solving -22 + a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + a + 22 + a2 = 0 + 22 Reorder the terms: -22 + 22 + a + a2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + a + a2 = 0 + 22 a + a2 = 0 + 22 Combine like terms: 0 + 22 = 22 a + a2 = 22 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. a + 0.25 + a2 = 22 + 0.25 Reorder the terms: 0.25 + a + a2 = 22 + 0.25 Combine like terms: 22 + 0.25 = 22.25 0.25 + a + a2 = 22.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (a + 0.5) equal to 4.716990566 and -4.716990566.Subproblem 1
a + 0.5 = 4.716990566 Simplifying a + 0.5 = 4.716990566 Reorder the terms: 0.5 + a = 4.716990566 Solving 0.5 + a = 4.716990566 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 = 4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 4.716990566 + -0.5 a = 4.716990566 + -0.5 Combine like terms: 4.716990566 + -0.5 = 4.216990566 a = 4.216990566 Simplifying a = 4.216990566Subproblem 2
a + 0.5 = -4.716990566 Simplifying a + 0.5 = -4.716990566 Reorder the terms: 0.5 + a = -4.716990566 Solving 0.5 + a = -4.716990566 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 = -4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -4.716990566 + -0.5 a = -4.716990566 + -0.5 Combine like terms: -4.716990566 + -0.5 = -5.216990566 a = -5.216990566 Simplifying a = -5.216990566Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.216990566, -5.216990566}
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