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Simplifying a2 + -20a + -55 = -3 Reorder the terms: -55 + -20a + a2 = -3 Solving -55 + -20a + a2 = -3 Solving for variable 'a'. Reorder the terms: -55 + 3 + -20a + a2 = -3 + 3 Combine like terms: -55 + 3 = -52 -52 + -20a + a2 = -3 + 3 Combine like terms: -3 + 3 = 0 -52 + -20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -20a + 52 + a2 = 0 + 52 Reorder the terms: -52 + 52 + -20a + a2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -20a + a2 = 0 + 52 -20a + a2 = 0 + 52 Combine like terms: 0 + 52 = 52 -20a + a2 = 52 The a term is -20a. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20a + 100 + a2 = 52 + 100 Reorder the terms: 100 + -20a + a2 = 52 + 100 Combine like terms: 52 + 100 = 152 100 + -20a + a2 = 152 Factor a perfect square on the left side: (a + -10)(a + -10) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (a + -10) equal to 12.328828006 and -12.328828006.Subproblem 1
a + -10 = 12.328828006 Simplifying a + -10 = 12.328828006 Reorder the terms: -10 + a = 12.328828006 Solving -10 + a = 12.328828006 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = 12.328828006 + 10 Combine like terms: -10 + 10 = 0 0 + a = 12.328828006 + 10 a = 12.328828006 + 10 Combine like terms: 12.328828006 + 10 = 22.328828006 a = 22.328828006 Simplifying a = 22.328828006Subproblem 2
a + -10 = -12.328828006 Simplifying a + -10 = -12.328828006 Reorder the terms: -10 + a = -12.328828006 Solving -10 + a = -12.328828006 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = -12.328828006 + 10 Combine like terms: -10 + 10 = 0 0 + a = -12.328828006 + 10 a = -12.328828006 + 10 Combine like terms: -12.328828006 + 10 = -2.328828006 a = -2.328828006 Simplifying a = -2.328828006Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.328828006, -2.328828006}
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