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Simplifying a = a2 + -22 Reorder the terms: a = -22 + a2 Solving a = -22 + a2 Solving for variable 'a'. Reorder the terms: 22 + a + -1a2 = -22 + a2 + 22 + -1a2 Reorder the terms: 22 + a + -1a2 = -22 + 22 + a2 + -1a2 Combine like terms: -22 + 22 = 0 22 + a + -1a2 = 0 + a2 + -1a2 22 + a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 22 + a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + -1a + a2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -1a + 22 + a2 = 0 + 22 Reorder the terms: -22 + 22 + -1a + a2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1a + a2 = 0 + 22 -1a + a2 = 0 + 22 Combine like terms: 0 + 22 = 22 -1a + 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. -1a + 0.25 + a2 = 22 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 22 + 0.25 Combine like terms: 22 + 0.25 = 22.25 0.25 + -1a + 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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