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Simplifying a2 + -7a + -38 = 0 Reorder the terms: -38 + -7a + a2 = 0 Solving -38 + -7a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -7a + 38 + a2 = 0 + 38 Reorder the terms: -38 + 38 + -7a + a2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -7a + a2 = 0 + 38 -7a + a2 = 0 + 38 Combine like terms: 0 + 38 = 38 -7a + a2 = 38 The a term is -7a. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7a + 12.25 + a2 = 38 + 12.25 Reorder the terms: 12.25 + -7a + a2 = 38 + 12.25 Combine like terms: 38 + 12.25 = 50.25 12.25 + -7a + a2 = 50.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (a + -3.5) equal to 7.088723439 and -7.088723439.Subproblem 1
a + -3.5 = 7.088723439 Simplifying a + -3.5 = 7.088723439 Reorder the terms: -3.5 + a = 7.088723439 Solving -3.5 + a = 7.088723439 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 7.088723439 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 7.088723439 + 3.5 a = 7.088723439 + 3.5 Combine like terms: 7.088723439 + 3.5 = 10.588723439 a = 10.588723439 Simplifying a = 10.588723439Subproblem 2
a + -3.5 = -7.088723439 Simplifying a + -3.5 = -7.088723439 Reorder the terms: -3.5 + a = -7.088723439 Solving -3.5 + a = -7.088723439 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -7.088723439 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -7.088723439 + 3.5 a = -7.088723439 + 3.5 Combine like terms: -7.088723439 + 3.5 = -3.588723439 a = -3.588723439 Simplifying a = -3.588723439Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.588723439, -3.588723439}
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