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Simplifying a2 + -1a + -63 = 0 Reorder the terms: -63 + -1a + a2 = 0 Solving -63 + -1a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -1a + 63 + a2 = 0 + 63 Reorder the terms: -63 + 63 + -1a + a2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -1a + a2 = 0 + 63 -1a + a2 = 0 + 63 Combine like terms: 0 + 63 = 63 -1a + a2 = 63 The a term is -1a. 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 = 63 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 0.25 + -1a + a2 = 63.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (a + -0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
a + -0.5 = 7.95298686 Simplifying a + -0.5 = 7.95298686 Reorder the terms: -0.5 + a = 7.95298686 Solving -0.5 + a = 7.95298686 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 = 7.95298686 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 7.95298686 + 0.5 a = 7.95298686 + 0.5 Combine like terms: 7.95298686 + 0.5 = 8.45298686 a = 8.45298686 Simplifying a = 8.45298686Subproblem 2
a + -0.5 = -7.95298686 Simplifying a + -0.5 = -7.95298686 Reorder the terms: -0.5 + a = -7.95298686 Solving -0.5 + a = -7.95298686 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 = -7.95298686 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -7.95298686 + 0.5 a = -7.95298686 + 0.5 Combine like terms: -7.95298686 + 0.5 = -7.45298686 a = -7.45298686 Simplifying a = -7.45298686Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.45298686, -7.45298686}
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