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Simplifying a2 + -5a + -42 = 0 Reorder the terms: -42 + -5a + a2 = 0 Solving -42 + -5a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -5a + 42 + a2 = 0 + 42 Reorder the terms: -42 + 42 + -5a + a2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -5a + a2 = 0 + 42 -5a + a2 = 0 + 42 Combine like terms: 0 + 42 = 42 -5a + a2 = 42 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = 42 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 42 + 6.25 Combine like terms: 42 + 6.25 = 48.25 6.25 + -5a + a2 = 48.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (a + -2.5) equal to 6.946221995 and -6.946221995.Subproblem 1
a + -2.5 = 6.946221995 Simplifying a + -2.5 = 6.946221995 Reorder the terms: -2.5 + a = 6.946221995 Solving -2.5 + a = 6.946221995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 6.946221995 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 6.946221995 + 2.5 a = 6.946221995 + 2.5 Combine like terms: 6.946221995 + 2.5 = 9.446221995 a = 9.446221995 Simplifying a = 9.446221995Subproblem 2
a + -2.5 = -6.946221995 Simplifying a + -2.5 = -6.946221995 Reorder the terms: -2.5 + a = -6.946221995 Solving -2.5 + a = -6.946221995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -6.946221995 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -6.946221995 + 2.5 a = -6.946221995 + 2.5 Combine like terms: -6.946221995 + 2.5 = -4.446221995 a = -4.446221995 Simplifying a = -4.446221995Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.446221995, -4.446221995}
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