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Simplifying (a * a) + -21a + -65 = 0 Multiply a * a (a2) + -21a + -65 = 0 a2 + -21a + -65 = 0 Reorder the terms: -65 + -21a + a2 = 0 Solving -65 + -21a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + -21a + 65 + a2 = 0 + 65 Reorder the terms: -65 + 65 + -21a + a2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -21a + a2 = 0 + 65 -21a + a2 = 0 + 65 Combine like terms: 0 + 65 = 65 -21a + a2 = 65 The a term is -21a. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21a + 110.25 + a2 = 65 + 110.25 Reorder the terms: 110.25 + -21a + a2 = 65 + 110.25 Combine like terms: 65 + 110.25 = 175.25 110.25 + -21a + a2 = 175.25 Factor a perfect square on the left side: (a + -10.5)(a + -10.5) = 175.25 Calculate the square root of the right side: 13.238202295 Break this problem into two subproblems by setting (a + -10.5) equal to 13.238202295 and -13.238202295.Subproblem 1
a + -10.5 = 13.238202295 Simplifying a + -10.5 = 13.238202295 Reorder the terms: -10.5 + a = 13.238202295 Solving -10.5 + a = 13.238202295 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = 13.238202295 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 13.238202295 + 10.5 a = 13.238202295 + 10.5 Combine like terms: 13.238202295 + 10.5 = 23.738202295 a = 23.738202295 Simplifying a = 23.738202295Subproblem 2
a + -10.5 = -13.238202295 Simplifying a + -10.5 = -13.238202295 Reorder the terms: -10.5 + a = -13.238202295 Solving -10.5 + a = -13.238202295 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = -13.238202295 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -13.238202295 + 10.5 a = -13.238202295 + 10.5 Combine like terms: -13.238202295 + 10.5 = -2.738202295 a = -2.738202295 Simplifying a = -2.738202295Solution
The solution to the problem is based on the solutions from the subproblems. a = {23.738202295, -2.738202295}
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