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Simplifying a2 + -1a + -21 = 0 Reorder the terms: -21 + -1a + a2 = 0 Solving -21 + -1a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -1a + 21 + a2 = 0 + 21 Reorder the terms: -21 + 21 + -1a + a2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1a + a2 = 0 + 21 -1a + a2 = 0 + 21 Combine like terms: 0 + 21 = 21 -1a + a2 = 21 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 = 21 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 21 + 0.25 Combine like terms: 21 + 0.25 = 21.25 0.25 + -1a + a2 = 21.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (a + -0.5) equal to 4.609772229 and -4.609772229.Subproblem 1
a + -0.5 = 4.609772229 Simplifying a + -0.5 = 4.609772229 Reorder the terms: -0.5 + a = 4.609772229 Solving -0.5 + a = 4.609772229 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 = 4.609772229 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 4.609772229 + 0.5 a = 4.609772229 + 0.5 Combine like terms: 4.609772229 + 0.5 = 5.109772229 a = 5.109772229 Simplifying a = 5.109772229Subproblem 2
a + -0.5 = -4.609772229 Simplifying a + -0.5 = -4.609772229 Reorder the terms: -0.5 + a = -4.609772229 Solving -0.5 + a = -4.609772229 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 = -4.609772229 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -4.609772229 + 0.5 a = -4.609772229 + 0.5 Combine like terms: -4.609772229 + 0.5 = -4.109772229 a = -4.109772229 Simplifying a = -4.109772229Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.109772229, -4.109772229}
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