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Simplifying 2a2 + -8a + -73 = 0 Reorder the terms: -73 + -8a + 2a2 = 0 Solving -73 + -8a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36.5 + -4a + a2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + -4a + 36.5 + a2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + -4a + a2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + -4a + a2 = 0 + 36.5 -4a + a2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 -4a + a2 = 36.5 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 36.5 + 4 Reorder the terms: 4 + -4a + a2 = 36.5 + 4 Combine like terms: 36.5 + 4 = 40.5 4 + -4a + a2 = 40.5 Factor a perfect square on the left side: (a + -2)(a + -2) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (a + -2) equal to 6.363961031 and -6.363961031.Subproblem 1
a + -2 = 6.363961031 Simplifying a + -2 = 6.363961031 Reorder the terms: -2 + a = 6.363961031 Solving -2 + a = 6.363961031 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 6.363961031 + 2 Combine like terms: -2 + 2 = 0 0 + a = 6.363961031 + 2 a = 6.363961031 + 2 Combine like terms: 6.363961031 + 2 = 8.363961031 a = 8.363961031 Simplifying a = 8.363961031Subproblem 2
a + -2 = -6.363961031 Simplifying a + -2 = -6.363961031 Reorder the terms: -2 + a = -6.363961031 Solving -2 + a = -6.363961031 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -6.363961031 + 2 Combine like terms: -2 + 2 = 0 0 + a = -6.363961031 + 2 a = -6.363961031 + 2 Combine like terms: -6.363961031 + 2 = -4.363961031 a = -4.363961031 Simplifying a = -4.363961031Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.363961031, -4.363961031}
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