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Simplifying a2 + -13a + -45 = 0 Reorder the terms: -45 + -13a + a2 = 0 Solving -45 + -13a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -13a + 45 + a2 = 0 + 45 Reorder the terms: -45 + 45 + -13a + a2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -13a + a2 = 0 + 45 -13a + a2 = 0 + 45 Combine like terms: 0 + 45 = 45 -13a + a2 = 45 The a term is -13a. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13a + 42.25 + a2 = 45 + 42.25 Reorder the terms: 42.25 + -13a + a2 = 45 + 42.25 Combine like terms: 45 + 42.25 = 87.25 42.25 + -13a + a2 = 87.25 Factor a perfect square on the left side: (a + -6.5)(a + -6.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (a + -6.5) equal to 9.340770846 and -9.340770846.Subproblem 1
a + -6.5 = 9.340770846 Simplifying a + -6.5 = 9.340770846 Reorder the terms: -6.5 + a = 9.340770846 Solving -6.5 + a = 9.340770846 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + a = 9.340770846 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + a = 9.340770846 + 6.5 a = 9.340770846 + 6.5 Combine like terms: 9.340770846 + 6.5 = 15.840770846 a = 15.840770846 Simplifying a = 15.840770846Subproblem 2
a + -6.5 = -9.340770846 Simplifying a + -6.5 = -9.340770846 Reorder the terms: -6.5 + a = -9.340770846 Solving -6.5 + a = -9.340770846 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + a = -9.340770846 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + a = -9.340770846 + 6.5 a = -9.340770846 + 6.5 Combine like terms: -9.340770846 + 6.5 = -2.840770846 a = -2.840770846 Simplifying a = -2.840770846Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.840770846, -2.840770846}
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